What should I be looking for when trying out running shoes? Local store lets me try the shoe and jog up and down the block, but they mostly feel the same to me. Is there some feeling or anything else specific I should be looking for?

If you're starting out, you can get away with daily trainers until you think you need to add more gear into your training.

You need to select a shoe that works for you. I don't know your fitness level but a good start is finding a good, durable daily trainer. These work well for low intensity and slow speeds that can withstand distances up to 20 or so km. You could use them for sprint sessions if you want.

A good way to research shoes is to watch YouTube channels that review the shoe. There are several good ones that conduct a thorough review.

Which MBA specialisation is a good option for me? I have a BE computer degree and working in the IT field.

Some shoes need a break in period to really get to know how the shoe will perform. Some are good right out of the box.

Fit. Heel lock. Bounce. Cushioning. Rebound. Energy return. Responsiveness at different speeds. Support.

Then you got the race day shoes. If you're competitive and wanting to hit a personal best, then getting a super shoe will help with your performance. These are really expensive. They're not made with durability in mind.

Is it okay if I am not interested to talk to any of my relatives as I saw the real faces in my brother's marriage as none of them helped us rather were a kind of disappointment and were talking bad?

Speed shoes are for that, speed. They usually have some form of carbon plate in the sole. They will feel awful if you're running below a certain pace, but feel great once you surpass that speed threshold.