how the coins are generated from air ?
No, you are basically allowed to send yourself the 6.25BTC block reward + transaction fees from a block, if you solved the PoW problem for that block through mining.
So yes, the coinbase transaction has no input, but 'out of thin air' would mean that you put nothing into it, while you did pay for energy & hardware to solve that PoW.
are exchanges have another type of blockchain running?
Everyone's running the same blockchain, otherwise it would not work.
Do note that the 'Coinbase exchange' has nothing to do with 'coinbase transactions' besides having named themselves after these transactions.