Prototypical examples vs edge cases
To start with, I must note that I believe it is most beneficial to identify and describe the prototypical examples of a phenomenon. Language is incredibly complicated, and there will almost always be edge cases, but most of the time you can come up with good explanations that cover 98% of the cases. We want helpful explanations, but sometimes trying to account for 100% of the cases prevents us from doing so. This is an ideological position, but I think it is still valuable working on these explanations even if they are not complete.
Arguments vs adjuncts
The first distinction we need to be clear on is between arguments and adjuncts. Arguments are the parts of sentences which verbs require. Adjuncts are optional. Here are some examples of arguments:
I kicked the ball.
I gave you a puppy. ("you" and "a puppy" are two arguments)
Here are some classic examples of adjuncts:
Last Tuesday I played soccer.
He slept very late at night.
I reluctantly gave you a puppy.
These phrases certainly do contribute to the whole meaning of the sentence, but they can be left out without changing the core sense of the verb. They can also be moved more freely around the sentence. For example, these two sentences are describing essentially the same kind of event, which is just located at a different point in time:
Last Tuesday I played soccer.
Last Wednesday I played soccer.
But these two are describing different kinds of events:
Last Tuesday I played soccer.
Last Tuesday I played golf.
Arguments can be essentially any word class (or phrase class):
Noun: I want a puppy.
Verb: I want to eat dinner.
Adjective: I feel hungry.
Adverb: I climbed up the mountain.
Preposition: I escaped from prison.
Whether a word (or a specific word sense) requires a noun phrase or a preposition phrase doesn't have anything to do with whether it's transitive or not, it is just what the verb itself requires, and it is not predictable.
Most of the time it is pretty easy to classify sentence constituents as arguments or adjuncts, but sometimes it's harder. In the following examples, the first has a clear adjunct. The second and third examples are not so clear. Tackling necessarily involves a second person, so it could be argued to be an argument. (Or that the argument is the whole of the phrase "tackling with my friend", with "with my friend" being a part of this participial phrase rather than a direct descendent of the verb practiced.) To complicate matters further, sometimes a phrase might seem obligatory when you think of its meaning, but syntactically it could still be an optional adjunct. The second example would seem like a simple adjunct, but if the third is in mind then it may feel more like an argument.
- I ate dinner with my friend.
- I played soccer with my friend.
- I practised tackling with my friend.
Most words have multiple related senses; it's actually quite rare for a word to only have a single meaning. The different senses of a word often require different kinds of arguments. As an example, these three sentences all have different senses of the word "read":
- I am reading.
- I am reading a book.
- I am reading a book to you.
The first conveys the activity of reading, but without indicating any particular focus. Even if I read two books, this verb indicates only one event. The second focuses on a particular book. If I started reading a different book then this event would end. The third means reading for another person, usually out aloud, and is ditransitive.
Because of polysemy you usually cannot classify a verb simply as transitive or intransitive, because some of its senses may be different.
We normally think of verbs as single words, but there are some verbs that are actually multiple words. (In other languages this is always the case: in some languages the core inflected verb will always be a generic word like 'do' or 'happen', and the specific detail of the action is given in another word called a coverb.) In English it is very common for a preposition or adverb to form part of a verb. Here are some examples:
to throw up
to look forward to
to make up (a story)
But it's not again, it's not always easy to classify them. The verb "jump" by itself does not have the sense of ending in a difference place, but the verbs "jump up" and "jump down" do. I think that they have a difference sense than 1, but do they constitute one sense "jump [direction]", or are "jump up" and "jump down" two separate senses? It's hard to decide.
- to jump
- to jump up
- to jump down
Elision refers to when words can be left out because they are clear from the prior context. This is different from different senses as discussed above: out of context the elided sentences would be unnatural and sometimes even ungrammatical.
- Will you come with us tomorrow?
I will (come with you tomorrow).
- I will have to tell her the news.
It's okay, I already told her (the news).
Valency: transitive and intransitive
A verb's valency refers to how many arguments it needs. We use the term intransitive for a verb that has only one (the subject) and transitive for a verb that needs two. Ditransitive refers to verbs that take three (but it's di- because there's two objects.) But remember that this categorisation is specific to each sense. Now things get trickier when you have sentence constructions that change the number of arguments (like the passive voice) or when words are elided (which I do not think changes whether a word is transitive or not.)
A word sense may require a particular word class for its arguments, but whether the word/phrase class is a noun or a preposition doesn't impact its valency: only the number of arguments does.
In the examples asked about in the question (yes we're finally ready!) both comply and follow are transitive. In fact they're probably transitive in all of their senses (I can't think of any counter examples.) But if you compare those two verbs with the very similar verb submit you can see that in terms of their valency, they are different. Submit can easily be used intransitively, but comply and follow probably cannot. (But maybe you can find some examples where they can.)
So for example, I could say about a very submissive and weak-willed person
He always submits. He always gives in.
And entirely out of context, we can understand that I'm talking about a submissive person. (Possibly submits is too formal and it may seem unnatural, but gives in should definitely be okay as an intransitive verb.) But if I said this out of context
He always complies.
You wouldn't understand what I was talking about. If we've been talking already about him and so the conversation has a particular context (talking about traffic rules, or his job, or the rules of his favourite sport) then this sentence is fine. But if we hadn't, then you would be wanting to ask "He complies with what?"