Generally yes,the iit's and nit's are the most most prestigious colleges of India. But private colleges like Bits pilani, bit and Anna University have also good rankings...

Dear
Yes, absolutely true. But some Engineering private colleges are more better than so of the government college.so it's better to choose the decision wisely.
All the best.

Yes it's true government engineering colleges are better than private engineering colleges in every aspect....government college gives better placements and they have experienced faculty....and a government college's  degree has more value than private college's degree..

Yes
Well reputated government engineering colleges are private.
Like nit or gft
Good placement record.
Good luck