Yes you can for this you have to appear for gate and you have to crack the cutoff for iit .By that you can get chance in iit.

Yes you can.

As said it doesnt mattrs alot if you do graduation from a very normal college but your masters should always be from a good place. M.Tech could surely be done from IIT if you pass GATE for the respective admitting year in this your graduation place doesnt matters. Prepare thoroughly for it.

All the best

Thankyou.