Computer Science and Engineering

No, because the closing rank for CSE in HIT after the 3rd round was 5030 last year.
So, you will not get.Try for other colleges.

No, you will not get any of the college which is mentioned above.

You cannot get admission in Heritage, IEM,Haldia but in BC Roy chances are very low for computer science. You have to wait till 3rd round.

With JEE, it's really hard for you to get any college unless you're from some category. With your other rank you may get some decent state government college for that please check Shiksha college predictor for exact predictions.
All the best.

Yes, you can do B.Tech CSE but you will not get any government college. Don't lose hope because of your rank. You can apply in private colleges. You can give entrance exam as well. Find the cut-off of previous years. Surely you will get admission but I will suggest you to do well in your B.Tech beca

Please tell your mark?

Chances are slim, though you have chance to get some decent government college through JEE itself try to get in those.
All the best.

I also had almost same rank as you 1578 (AIR_OBC). I will suggest you to select NITK Surathkal IT. Even CSE at Allahabad is also a very good option if you are from UP. So if you want to stay near to home then go for CSE at NIT Allahabad otherwise come to NITK, Surathkal in IT.

Yes, it is good for CSE. If you will do your best then you will get a good placement. Many companies come here which give packages more than 10 LPA. So there are chances that you will get good package. Also academic of UPES is good.