B.Tech

Yes, you can pursue it and secure a good job as well.
MITSkills, Pune (Advanced Post Graduate Programme in Piping Design and Engineering with PDMS and CAESAR-I)
Vishwakarma Institute of Technology (VIT) - Pune
Asian Academy of professional training (AAPT) - Pune
Indian Institute of Technology, Bombay (I

It is advisable to continue your stream of ME. As this give you in-depth knowledge of your graduation and helps you to land up in core engineering jobs. But nowadays the combination of "B.Tech + MBA" is really in great demand by companies. So it may be the wise choice if do MBA after graduation. Alt

Yes you can get into Amity University, Mumbai through lateral entry, follow the official link below for details:
http://www.amity.edu/lateral/

Yes, you can if you get your all original certificates back such as transfer certificate, migration certificate and if you get them then you have to appear in JEE.

Study and Lead Educational and Welfare Society, Bangalore does not provide regular B.Tech course, for details check the link below:
http://www.studyandlead.com/programmes-1.php

Correspondence BE is not a valid course and you might not be able to apply in many companies for job, I would recommend you to pursue regular BE course from a good institution.

Qualification is 10+2 with minimum 75%, you need to qualify national or state level engineering entrance exams like JEE, BITSAT, MHTCET, VITEEE, etc. to get in a top B.Tech aeronautical engineering college.