How to handle students' disrespectfulness?

For depression, seek professional help.

Otherwise,

Few things look alarming to me. The whole of the issue also seems like a conflict and we are only presented with your side which does not include factual statements rather your interpretation of events. (i.e. they are being disrespectful) Some alarming things on your side:

After the chairman spoke to me, I started talking to my students softly (more than needed)

demeaning attitude towards your students.

I tried many other ways to engage them. But the problem is that they think the subject is of no use. I have told them of many applications, but I think they won't realize it now.

I personally think they have the right to be uninterested if the course is mandatory. You can't force-teach people. If you find people's non-engagement distracting, you can try to provide outside of class resources, class videos etc. and make attendance optional.

But one student is insulting me from day one. He has issue on everything, on assignment.

criticism is not disrespect. He has the right to voice his concern if he thinks there is a problem with the assignment.

Instead of accepting his mistake, he was fighting with me that I didn't formulate the question correctly.

There is nothing wrong with contesting a grade given. Some, if not most, schools even mandate that there is a session in which students can dispute their exam grades or ask for an independent evaluation.

So I sent that question to my assistant professor. He verified and said that the question is clear.

Not enough to reach a conclusion.

Overall, your text leave me with the impression that you might very well be at fault here. I can't also say with certainty that your attitude described above is respectful towards your students, at least not on a fundamental level.

About that one student, you might demand a disciplinary hearing in which you get to present your side and he gets to present his side (hopefully). Eventually, an impartial body of staff decides if he needs to be punished. I don't think with what you have stated here anyone can reach a clear cut conclusion. However, as Bryan Krause pointed out, this might have negative consequences for you if your claims and interpretation of events are not within a reasonable range of the factual events.