B.Tech

Yeah, embedded course are too good for ECE engineering it will also be a topic during your engineering and it will provide better career in this field, you can get the job easily by this course.

I think your question is wrong you 140 cut off marks in entrance exam, by the way I will give a link that will help you to find the college according to your rank:
https://www.resonance.ac.in/reso/news/JEE-Main-Branch-Predictor.aspx

T.I.M.E is the best institute for you.

Definitely B.Tech is better than B.Sc because it has good scope than B.Sc, if you go for B.Sc you'll get low salary and you can go for research but if you go for B.Tech, you can go for anything you need and you'll get a good salary.
choose wisely.

It will depend on your rank that you secured in the entrance exam. If you tell me the name of the entrance exam in which you appeared and the rank you secured then I can suggest you some colleges.

You are eligible to seek admission in MS or M.Tech in Aeronautical Engineering after completing B.Tech in Aeronautical Engineering. MS in Aeronautical Engineering in top engineering colleges such as MIT, USA will help you achieve your target to work in NASA.

It is difficult to say on the basis of your JEE Mains score but still try for institutions in both Punjab or Haryana like Chandigarh University, etc. As a whole, I would say that work hard & score better next year in JEE Mains.

Yes, you can take direct admission in JSS.