IIT Madras - Indian Institute of Technology

Yes, you can. But you need to score good percentile in the entrance tests.

It's an average college with decent placements, check out the link for details :
https://www.shiksha.com/Iitm-International-Institute-Of-Technology-Management-Murthal-Sonepat-institute-college-listingoverviewtab-32556

There are very few core companies in aerospace that comes for placements and also their package is not that attractive. But there are good options if you want to go for higher studies. Most of the students of aerospace engineering of IIT Madras go for ms and PhD abroad. The options their are great. So if you want to pursue aerospace engineering please keep your options open for higher studies as well.

There is no cg cutoff for branch slide but there is a cg cut off for branch change. You just have to make sure that you pass all your courses in the first semester for a branch change. Branch change and slide happens right after the first year so you need to apply in the first semester itself. For branch change you need to be in the top 3 or 4 class positions after your first semester.

Well I am not really sure about the rank. It also depends on the category you belong to. Basically the opening n closing ranks for iitm aerospace specialisations vary. Kindly go through the brochure for more details.

BBA is not good for anywhere except if you go for integrated MBA.

IITs are good