Lambie's answer to "Counter" in "countersteering" an adverb or adjective? which was recently re-opened should be undeleted promptly. I see no valid reason why it was ever deleted. One might disagree with the answer, but it was a reasonable answer from a high-rep user, and it is likely to be useful to the OP, if s/he ever reads it. I ask that this answer be undeleted promptly. If others do not like it, downvote it as usual. I would vote to undelete this, but as it was deleted by a mod, I cannot do so.
The first part of the OP's question, or "first question" if you want to call it that, clearly depends on a misunderstanding that individual elements of words, which might have originated as separate words, have their own parts of speech, and that a compound constitutes two different words.
Lambie's answer includes the statements:
... We don't separate out words from existing words. Worldwide is one word so in it world and wide don't have functions. ...
It seems to me that this responds pressingly to to the OP's confusion. Another user might have responded in a somewhat different way, but it does address the issue in the OP's question, and so is a legitimate answer, in my view. A I see it, it would still be a valid answer if the second part of the question were edited away.
Now, as to whether the question as posted constitutes multiple questions in the sense that would leave it off-topic: I am inclined top say that it was not. Both parts are clearly addressing the text string "countersteer". In both, the OP is trying to understand what happens grammatically when a word is created out of other words. I think, particularly when addressing such a basic confusion, it is more useful to treat this as a single question with multiple aspects. These aspects are best addressed within a single answer, in my view.
I will add that deleting an answer that is clearly attempting to address the question, and all of the statements in which are in fact correct, even of one things the answer does not properly address the question, or adds additional explanations, is usually unwise. Downvoting or commenting or both seem more useful, as a rule.
I'm the mod who deleted Lambie's answer.
When I deleted it, it appeared to me that it was not answering the OP's question, as Lambie had misread. So I deleted it as "Not an answer" and left two explanatory comments. Lambie got upset with me, but they hadn't addressed the issue in my comment, so I didn't respond -- a mod shouldn't undelete answers just because a user it upset about it.
I talked with Glorfindel, and they pointed out that Lambie's answer addresses the OP's second question, "Additionally what category of a word this is? Is it a compound verb or something else?" When I'd read that, I'd thought it was a continuation of the question about "counter-", so I hadn't realized the OP had actually asked a second question about "countersteer" as well, which meant Lambie's answer did address the OP.
That left me with a new problem, which was the question was now off-topic because it asked two unrelated questions in one. Normally, in a situation like that, I'd remove the second question and leave a comment to the OP reminding them that although the second question arises from a component of the first, it is a separate question, that we have a rule against asking two questions, and that if the second question is important enough, they could open a new question and ask it there.
But with Lambie already rallying protest support from other users, I figured it would fan the flames at that point to remove that second question because it would also invalidate Lambie's answer. So, what to do??
I was talking with Glorfindel about how we should respond, when we noticed this demand on Meta that we undelete the answer. As it stands, Lambie's answer is now on topic, so I've undeleted it. But if we apply the rule of not asking two questions at once, that answer will become off-topic again. And here we are.