Let say you want to sell someone some btc. But you want them to send the btc to your exchange account btc address whether its bittrex, binance or other exchange accounts. Is that generally safe or not?
The other thing is i know with bittrex/binance, they give you the btc address to send btc to. But could you generate a new btc address? If so, would there be any conflict with any btc you already have in that bittrex/binance address?
Just like the earlier poster has said it just like using a wallet that you own that generates address as you want but in this case its being generated for and there is always a connection that any fund sent to that particular address is shown in your profile and no one else. The only concern here is you might not be able to use that same address for a long time because, that same address that is being generated for you, might have been used by someone else at some time and after you, it will be assigned to someone else. You can confirm this when you check the address on the blockchain.
On the other question, each wallet is assigned to your profile which can generate a new wallet the moment you dont want that wallet you can generate another address but on the same wallet.