Computer Science and Engineering

Yes, for computer Science, it is not mandatory to have computer in class 12th. You only Have to qualify JEE. And without computer in your 12th, you can get computer science but maths is mandatory in class 12th. Then, you will get admission in engineering.
Good luck.

You are not eligible for getting a seat in AU in your desired groups. In Amritha, you may have a chance.

With this AEEE rank of 7000+ you can get ECE department with a minimal chance of not getting it. It is better if you get it in Coimbatore campus rather than Bangalore campus of Amrita.

In all honesty, it depends on the pace of work done at your institute. There is a slight chance majority of your degree won't be completed at your own campus, but highly unlikely that you'll complete 4 years not being at your campus.
Again, it depends more at the pace of work and how fast the governm

Karnataka Examination Authority (KEA) releases KCET 2018 cutoff for admission to the participating institutes of the entrance examination. It must be noted that the KCET cutoff 2018 will be different for different engineering institutes and different engineering programmes as per the different categ

Your score is good, but may not be enough to get a rank under 1000 (not very sure though, there are good possibilities of getting the same). But you have nothing to fear, you can get any branch of your choice.

Yes, of course. You can get a seat in CSE branch even in Visakhapatnam campus with your rank.
Tuition fee=2,42,000/-
Special fee=30,200/- per an academic year.

Which reputed institute are you talking about?