Shall I do B.Tech first year with JEE coaching?

If you wish to do that then you can prepare simultaneously with full concentration. As the college life is full of new things, new environment, society, friend circle keep in touch with that being social is not wrong but you must keep this in mind that you are preparing for tough exam so be focused

You can do if you think you can manage it. Usually it is very hard to manage in college as there will be assignment, project, mid sem & end sem exams, functions, etc. Go for it if your basic is strong and have strong hold on each subject. Don't go for college is your preparation is not good.

Yes, you can do that so that you can get admission in a better college next year.

It's really very tough. If you are planning to change the college then pull up your socks from now only. Because the institute will give lots of load and works. Assignments, Journals, Exams will all screw you up. So first of all if you have time in the weekend, join coaching classes for JEE Main in