Jain Deemed-to-be University, Bangalore

I don't know about Jain University, Bangalore so I cannot comment on this. But here in UPES, BBA course is above average.
If you compare placements with the fee, you will not be much happy. But I know some seniors here who have started their own start-ups.
So you will learn a lot of things here.

Go for Jain University without any second thought. Had you opted for B.Tech, UPES would have stood out.

Yes, you can still apply for it. Admission is on. Go to https://www.jainuniversity.ac.in/Admissions-in-Top-Colleges-of-Bangalore-India-offered-by-Jain-University.php.
All the best.

Yes, you are eligible for that.

Yes, you can get admission as the minimum eligibility criteria for the same is pass in the 12th standard from recognized boards like CBSE/ISC/PUC or equivalent board.

Yes, you can get lateral entry after completing your diploma from Arka University. On the basis of last year's percentage of diploma, you will get admission.
Best of luck for your future and if there's any query, feel free to ask.

Amity is the best amongst these 4 to pursue BBA. As its a renowned University and provide really good placments as well.

Please check for your eligibility for a PG course in Forensic Science from the criteria mentioned below:
Eligibility for PG in Forensic Sciences:
Minimum eligibility criteria for PG in Forensic Science course may vary across institutes. Primarily, the criteria include:
Bachelors degree in science/ engineering / pharmacy/ medicine, obtained from a recognized university.
A minimum aggregate score of 60% at the level of graduation. Regards.