IIT

It depends on your category. If you belong to SC/ST category, then don't worry. If you belong to OBC or general category, then you appear for improvement exam.

If you are already doing any Bachelor's course, so you can't but you can still opt for Masters from IIT.

While it's a fact that most of the universities abroad only know IITs, you still have a good chance to get admission on the basis of your strong profile that includes researches, publications, internships, leadership projects, etc. Letter of recommendations from your professors employer will also he

Yes, you are eligible as NIOS degree is valid for JEE examination.

No, you are not eligible.
Eligibility criteria for IIT JAM
All candidates admitted through JAM should have a Bachelor’s degree.
At least 55 percent aggregate marks, without rounding off (taking into account all subjects, including languages and subsidiaries, all years combined) for general and OBC/NCL

You may register with any of the websites to get admission notifications. Many coaching centers also provide this service.
Please check the below mentioned link:
http://entrance-exam.net

Every student have its own learning and grasping capacity, time table is a person specific thing. You are the best judge of your strengths and weaknesses and the amount of time you need to spend daily. Keeping that into consideration design the time table.

It depend, in which stream you want to take admission. But, approximately you need 170 marks for top NITs.