Indian Institute of Technology, IIT Bombay

Cut off and rank varies yearly depending upon number of students appearing in the examination, difficulty of exam and the highest marks scored, so to predict minimum rank is not possible, maybe you can check last few years rank and have a rough idea about the same.

Yes one can get placed abroard placement but companies less in campus selection so one must have a good grade point and good resume. Also you can apply on your own and get a job.

Class 10th percentage has no relation with admission in IIT. 12th percentage must be greater than 75% to qualify for giving JEE. Depending on your JEE All india Rank colleges are alloted. All the branches at IIT Bombay close around 4000 AIR. So one must have AIR under 4000 to get IIT Bombay.

Yes JEE is necessary to get admission in IIT. Percent changes each year depending on the toughness of paper but one must have AIR under 1500 to get aerospace in IIT Bombay. In my year i.e 2014 aerospace closed at 1800 AIR and mark required for AIR 1800 was around 210/360 which is 60% but it changes each year depending on Paper.

Aerospace Branch is available in IIT Bombay Kanpur and Kharagpur. At bombay cutoff rank is around 1500 at kanpur it close at around 2500 and at Kharagpur it closes around 3500 so one must have AIR under 3500 to get aerospace in IIT.

10th percentage is not required but you must have more than 75% in 12th in order to give IIT exam.After the exam 12th percentage is not considered and seat allotment is based on your All India Rank.

Yes you can but I don't think B Tech will be enough for that and you should also complete MS after BTech.