Mechanical Engineering

Yes, you can definitely join Indian air force after completing degree in mechanical engineering. Top colleges of aeronautical engineering in India are:
1. Indian Institute of Aeronautical Engineering, Dehradun
2. Indian Institute of Space Science and Technology, Thiruvananthapuram
3. PEC University of Technology, Chandigarh
4. Sathyabama University, Chennai
5. UPES, Dehradun

Yes, America is a good option to pursue aeronautical engineering but you should not rule out the option of studying from India as well. India is a growing country in this field and people are getting very good pay as well. I can list down a few colleges I know of in India:
• Indian Institute of Aeronautical Engineering, Dehradun
• Indian Institute of Space Science and Technology, Thiruvananthapuram
• PEC University of Technology, Chandigarh
• Sathyabama University, Chennai
• UPES, Dehradun

Aeronautical engineering is more of a specialized stream where you will limit your job opportunities to the respective segment of industry. Thermal Engineering, Nano Technology, Fluid Mechanics, Industrial Engineering etc. are also in demand. But if you aim to push yourself into the academic stream, then any post graduation will do.

Even with a B.Tech, you can put yourself into the military track.

Hi,
There are various courses available in design like Web Designing, Graphic Designing, Interior Designing and Fashion Designing and if you are interested in Design courses then you should make survey of institutes, training centers and coaching classes in Ahmedabad as it is one of leading cities providing the courses of designing.

Of course it is. Mechanical engineering is a developing field and you can get good options for job and higher studies depending on your skills and expertise.

If you have interest in accounting/share and debentures, then go for finance. It also have flavor of mathematics.
If you have good convincing power, then go for marketing.
If you like to deal with people, then go for HR.
Operations is much suited for people from manufacturing.
There are some more discipline like financial engineering (FE). If you are good in mathematics, than you can opt for it. Also, FE is a less known in India and it is very much in demand. IFMR and one or two IIM runs this course.
Data science is another discipline which is booming. It also needs mathematics plus some hands on programming.

Yes, it is a better choice.