Dual

Yes, BCA+ MCA is a hot career now a days.

I would say IIIT, Allahabad, since it has a better reputation in terms of placement and infrastructure. Both are really good choices and there is no doubt about that though.

First of all, it is not BBA+MBA its IPM. You can get admission here by cracking the Aptitude test and Personal interview. Good luck.

Yes, for sure.
You don't even need to opt for dual degree course, you can get CSE in non-integrated course too, I guess.

If you want to get into purely technical side, then B.Tech + M.tech is better. But, if you want to have knowledge about management too, for better progress and all round knowledge and success, then go for B.Tech + MBA. Both of them have good career prospects depending on your choice and interest. However, many people opt for B.tech + MBA to be an all-rounder.

check the complete detail related to college and CSE branch in the link provided
https://www.shiksha.com/university/jaypee-institute-of-information-technology-noida-20383

No. There is no provision of dual degree as such. But you can go for dual specialization. Thanks.