(1) Why people use comments to answer the questions?
They shouldn't. This bypasses the voting mechanism; further, popular comments are often more visible than answers. The photography stack has a nice write up of why answers-in-comments are discouraged.
I can't quite follow the rest of your post, but I'll try to break this down.
(2) How do moderators handle answers in comments?
This is tricky. Some of the possible ways we can deal with answers-in-comments include:
- Encouraging authors to turn answers-in-comments into proper answers (everyone can do this, not just mods!)
- Move answers-in-comments and other off-topic comments to chat (the system only allows us move comments to chat once per post)
- Linking this FAQ which warns people that future answers-in-comments may be deleted
- Deleting answers-in-comments
- Declining to take any action
Determining which of these to use in a given case is a tricky business: comment-writers get angry when we delete their comments, but answer-writers get angry when we don't! We had some discussion of this a year ago, and while we did arrive at some general guidelines, we generally tailor our approach to each situation.
That said, there is no automatic answer-in-comment detector: if no one raises a flag, and we mods don't happen across it ourselves, then no action will be taken. This is one reason why it might appear that answers-in-comments are allowed.
(3) How do moderators handle comments in answers?
In my experience, most are extremely low-quality and are just deleted. In rare cases, we can convert answers to comments (but not the other way around)
(4) What I mean is: Instead of using a comment, I used the answer to try to contribute a question. I advised a site with academic research tools (it was a tool to discover the network of existing connections with a specific academic text), but my answer was quickly denounced and my contribution was seen as website marketing!
So in fact, this example really has nothing to do with the distinction between answers and comments!
I believe you are referring to this deleted answer (link for users with >10K reputation). In this case, the user had asked some specific questions about Google Scholar. You ignored these questions and wrote:
Although Sorry if my answer isn't such precise. However, I think everyone needs to know this website. That is a wonderful tool to follow and do the net of bibliography that apparently you want with Google Scholar features. [url redacted]
This does look a lot like spam. You didn't address any of OP's specific questions, instead recommending a totally different tool with no justification. I believe you when you say that you are not spamming, and I'm sorry you had this negative experience. However, if you are going to recommend a tool, you need to be very specific about why the tool solves OP's specific problem. We get a lot of spam here (often for predatory tools, journals, or conferences) and so it is natural to question the motivation of those who recommend a particular tool (and even moreso when the author is a new user).