"But what happens when you buy any crypto in an exchange? For example you in Coinbase you can generate as many addresses you want , but what are these? These are basically your Public Keys which can be shared. How about your private keys on coinbase exchange?"
I think they have control over the private keys and they won't give you access to it, because if they did then they bitcoin in your wallet could be withdrawn and you could blame them for it, so they kinda keep the private key to protect themselves from possible legal issues. I also think that a great deal of these exchanges have a certain amount of bitcoin in cold storage and the amount of bitcoin that they sell on the exchange shouldn't in theory exceed the amount of bitcoin that was deposited into their main wallet for that day or the amount that they have in cold storage. That being said, I don't think anyone except the people working at the exchange would know for sure.
Kinda related, but not directly related:
this is about using multisig on your wallet to add security.Thanks for an interesting post and for the like on my post. I started following you! Will stay in contact.