JEE Advanced

Cut-off is not yet declared by the authorities. Wait for the results.

Yes you are. You might even get your preferred course.

280 is a decent score. State your AIR or use Shiksha college predictor service.

It will depend on the cut-off marks of Advanced and only from that, you will be able to get the desired rank.

Yes you're eligible if you qualify JEE Advanced than you can give AAT exam, center would be the nearest zonal IIT.

You can see last year cutoff here:
https://www.shiksha.com/b-tech/articles/iit-qualifying-marks-for-jee-advanced-2018-released-blogId-17121

In my opinion, you should drop a year to get a deep knowledge of your subject, so that you can easily get a top NIT or IIT. Also, after that, you need not worry about your college if you don't get a top NIT because you would have a satisfaction that you know.

As you told that you have interest in every field I think you are an all-rounder. Jokes apart, all these courses are professional courses. You can't do this and that, and my best opinion is that choose as per your interest. And choose wisely. At this rank and mark, you can't get IIT.

IIT tag is surely worth a year but only if you are willing to sacrifice most of the things. Hard work always pays. But on the other hand, if you feel that NIT is worth it, then you should give it a try.

As you are in general category, you may not get high-level branches. But still, keep on trying till the last round.
All the best.