Degree

Yes,
Shri Vaishnav Vidyapeeth Vishwavidyalaya is a private university established under Madhya Pradesh NIJI Vishwavidyalaya Adhiniyam in 2015:
1. SVITS.
2. SVIIT.
3. SVITx.
These 3 are engineering colleges which come under SVVV.
Yes, SVVV gives their own B.Tech degree.

Yes. With the passing of IIM bill IPM has become a degree granting course. So the students now get an bsc in foundation management degree for undergraduation and an MBA degree further.
All the best.

For direct second year, fill the admission form from DTE .
For reference, put college code 6179.

Your class 12th mark would be a cause of concern, but try applying in a few private colleges.

No, St. Xavier's College does not provide any degree or specialization in graphic design.

To be honest, yes, it is definitely going to have an effect on your admissions. You have to score very high in CAT to get a decent college and also be prepared with a very good and genuine reason as to why you have so many backlogs.

MBA can be achieved after any course of graduation. But if you want to do your masters in Finance, then B.Com is the way ahead. If not, then you can go with BBA. You will get some idea about the field of business administration. But again, I would say it hardly matters. Find out your personal choice of interest and then, MBA will follow accordingly.