All four of your examples are compound sentences, which permit linking commas:
A compound sentence is composed of at least two independent clauses. . . . The clauses are joined by a coordinating conjunction (with or without a comma), a correlative conjunction (with or without a comma), a semicolon that functions as a conjunction, a colon instead of a semicolon between two sentences when the second sentence explains or illustrates the first sentence and no coordinating conjunction is being used to connect the sentences, or a conjunctive adverb preceded by a semicolon.
As @aurora notes, we commonly use commas with coordinating conjunctions except when linking very short and closely-related clauses, and even then it's never incorrect to use the comma. Here's how your sentences parse, with some additional notes.
Clause 1: He is a great player.
Clause 2: He prefers to play Counter-Strike.
Compound: He is a great player, and he prefers to play Counter-Strike.
Because both clauses have the same subject, you could could naturally replace and he with a relative pronoun: “He is a great player who prefers to play Counter-Strike,” making it a complex sentence instead of a compound.
Clause 1: John joined the Army.
Clause 2: George joined the Marines.
Compound: John joined the Army, and George joined the Marines.
This is a straightforward example of a compound sentence. Because both clauses are short and similar, you could omit the comma if you prefer.
Clause 1: Yes.
Clause 2: What is the problem?
Compound: Yes, and what is the problem?
Here, Yes is a special kind of clause called a pro-sentence.
Clause 1: I called John, my brother.
Clause 2: Now I'm speaking with him.
Compound: I called John, my brother, and now I’m speaking with him.
In this case, the phrase my brother is in apposition, so it must be set off with commas regardless of the structure of the rest of the sentence.