Mechanical Engineering

You can apply for b.tech mechanical degree programme and in higher education i.e m.tech you can choose automotive design as an specialization.

choose electric

instead of droping a year to study all subjects ,you should go for APPEARMENT EXAM for the specific subjects in which you failed to score good marks and Go for B.tec Mechanical which is already a very good decision for a bright future.
afterall there is no wise in droping a year to study everything again.
Gain knowledge about one of the best opportunity given to you by filling your appearment form and go ahead
good luck

Not at all.the recruitment depends on how well you perform in interview and not on gender.you will just have to show the recruiters that how badly you want to be a mechanical engineer.it also depends on your performence in btech upto some extent.

I think mechanical is easy than electrical.selecting the branch is very difficult . so my suggestion once go through the syllabus of both Electrical and mechanical topics and depending on the take a decision .
When it comes to Ms in us and M.tech in India . I prefer Ms but not in US , it is Germany ,Because for mechanical Germany is better . Even m>tech in India is good if you crack gate exam and get a seat in IIT/ NIIT.

Placements are not that good for mechanical . But most of the students of ME go for GATE exam then to PSUs or for further studies(m.tech)