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Different tenses are not the reason why that is a compound sentence. Further analysing the sentence "Hockey players are careful but they still get hurt often." you can split it into 2 independent clauses, connected by the coordinating conjunction "but".

Once that is done, it is simple to spot 2 subjects, first one being "players", and the second one being "they".

Also, to answer your question, changing tenses or the verb doesn't make this sentence simple—because it still has two independent clauses.

On the other hand in this example

She cooks very well and has a lovely cafe.

You do not have two(or more) independent clauses—it is not a compound sentence. There is one subject, and only one predicate. The predicate is marked in bold, it is something called a compound predicate.

She cooks very well and has a lovely cafe.

Here, "very well" is just an adverb. I can see how it can cause some confusion when placed like this.

There are some more examples of this same situation from here

Adam lives in Bangor and speaks Welsh.

The telegram was late but contained exciting news.

They need to absorb nitrogen and keep above 20 degrees.

EDIT: If the punctuation is done correctly, there is nothing incorrect about adding or omitting one subject.

Just like you stated

She cooks very well, and has a lovely cafe.

is incomplete, but

She cooks very well, and she has a lovely cafe.

is a grammatically correct compound sentence. Note that you have to use a comma here. (Comma is always used to separate independent clauses)

Assume the following (simple) structure of a sentence:

Subject + Predicate, subordinating conjunction + Subject + Predicate.

Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

Subject + Predicate + subordinating conjunction + Predicate.

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you add.

EDIT: Removed the first part of my answer.  (The entire answer becomes too long)

There is nothing wrong with transforming sentences the way you explained.

Hockey players are careful, but they still get hurt often

is equally correct as

Hockey players are careful but still get hurt often

Assume the following (simple) structure of a sentence:

S + P, SC + S + P.

Where S, P, and SC represent Subject, Predicate, and Subordinate Conjunction respectively. Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

S + P + SC + P

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you add.

She cooks very well and has a lovely cafe.

becomes

She cooks very well, and she has a lovely cafe.

Different tenses are not the reason why that is a compound sentence.

Further analysing the sentence you can split it into 2 independent clauses, connected by the coordinating conjunction "but".

First clause:

Hockey players are careful

Second clause:

They still get hurt very often

You do not have one subject, you in fact have 2 subjects in this case. "They" is the subject of the second clause.

Also, to answer your question, changing tenses or the verb doesn't make this sentence simple—because it still has two independent clauses.

On the other hand in this example

She cooks very well and has a lovely cafe.

You do not have two(or more) independent clauses—it is not a compound sentence. There is one subject, and only one predicate. The predicate is marked in bold, it is something called a compound predicate.

She cooks very well and has a lovely cafe.

Here, "very well" is just an adverb. I can see how it can cause some confusion when placed like this.

There are some more examples of this same situation from here

Adam lives in Bangor and speaks Welsh.

The telegram was late but contained exciting news.

They need to absorb nitrogen and keep above 20 degrees.

EDIT: If the punctuation is done correctly, there is nothing incorrect about adding or omitting one subject.

Just like you stated

She cooks very well, and has a lovely cafe.

is incomplete, but

She cooks very well, and she has a lovely cafe.

is a grammatically correct compound sentence. Note that you have to use a comma here. (Comma is always used to separate independent clauses)

Assume the following (simple) structure of a sentence:

Subject + Predicate, subordinating conjunction + Subject + Predicate.

Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

Subject + Predicate + subordinating conjunction + Predicate.

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you omit.

Different tenses are not the reason why that is a compound sentence. Further analysing the sentence "Hockey players are careful but they still get hurt often." you can split it into 2 independent clauses, connected by the coordinating conjunction "but".

Once that is done, it is simple to spot 2 subjects, first one being "players", and the second one being "they".

Also, to answer your question, changing tenses or the verb doesn't make this sentence simple—because it still has two independent clauses.

On the other hand in this example

She cooks very well and has a lovely cafe.

You do not have two(or more) independent clauses—it is not a compound sentence. There is one subject, and only one predicate. The predicate is marked in bold, it is something called a compound predicate.

She cooks very well and has a lovely cafe.

Here, "very well" is just an adverb. I can see how it can cause some confusion when placed like this.

There are some more examples of this same situation from here

Adam lives in Bangor and speaks Welsh.

The telegram was late but contained exciting news.

They need to absorb nitrogen and keep above 20 degrees.

EDIT: If the punctuation is done correctly, there is nothing incorrect about adding or omitting one subject.

Just like you stated

She cooks very well, and has a lovely cafe.

is incomplete, but

She cooks very well, and she has a lovely cafe.

is a grammatically correct compound sentence. Note that you have to use a comma here. (Comma is always used to separate independent clauses)

Assume the following (simple) structure of a sentence:

Subject + Predicate, subordinating conjunction + Subject + Predicate.

Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

Subject + Predicate + subordinating conjunction + Predicate.

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you add.

Different tenses are not the reason why that is a compound sentence.

Further analysing the sentence you can split it into 2 independent clauses, connected by the coordinating conjunction "but".

First clause:

Hockey players are careful

Second clause:

They still get hurt very often

You do not have one subject, you in fact have 2 subjects in this case. "They" is the subject of the second clause.

Also, to answer your question, changing tenses or the verb doesn't make this sentence simple—because it still has two independent clauses.

On the other hand in this example

She cooks very well and has a lovely cafe.

You do not have two(or more) independent clauses—it is not a compound sentence. There is one subject, and only one predicate. The predicate is marked in bold, it is something called a compound predicate.

She cooks very well and has a lovely cafe.

Here, "very well" is just an adverb. I can see how it can cause some confusion when placed like this.

There are some more examples of this same situation from here

Adam lives in Bangor and speaks Welsh.

The telegram was late but contained exciting news.

They need to absorb nitrogen and keep above 20 degrees.

Different tenses are not the reason why that is a compound sentence.

Further analysing the sentence you can split it into 2 independent clauses, connected by the coordinating conjunction "but".

First clause:

Hockey players are careful

Second clause:

They still get hurt very often

You do not have one subject, you in fact have 2 subjects in this case. "They" is the subject of the second clause.

Also, to answer your question, changing tenses or the verb doesn't make this sentence simple—because it still has two independent clauses.

On the other hand in this example

She cooks very well and has a lovely cafe.

You do not have two(or more) independent clauses—it is not a compound sentence. There is one subject, and only one predicate. The predicate is marked in bold, it is something called a compound predicate.

She cooks very well and has a lovely cafe.

Here, "very well" is just an adverb. I can see how it can cause some confusion when placed like this.

There are some more examples of this same situation from here

Adam lives in Bangor and speaks Welsh.

The telegram was late but contained exciting news.

They need to absorb nitrogen and keep above 20 degrees.

EDIT: If the punctuation is done correctly, there is nothing incorrect about adding or omitting one subject.

Just like you stated

She cooks very well, and has a lovely cafe.

is incomplete, but

She cooks very well, and she has a lovely cafe.

is a grammatically correct compound sentence. Note that you have to use a comma here. (Comma is always used to separate independent clauses)

Assume the following (simple) structure of a sentence:

Subject + Predicate, subordinating conjunction + Subject + Predicate.

Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

Subject + Predicate + subordinating conjunction + Predicate.

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you omit.