I mean, I get it, you never show your private key to anybody. Easy enough.
But when do you use it?
If you want to withdraw your money from the exchange, you use your public key. But then, if you wanna send your money back to the exchange, you use the public key from your exchange's wallet?
So using your private key would be limited to getting your money out of the system (cashing out)? Because even if you purchase something, it makes sense (at least from my completely uninformed point of view) to use the seller's public key to make the payment...
Can anybody please help me out? Thank you all in advance.
What you give the exchange at withdrawing is your address, not your public key. When you send coins away, you send them to an address.
The private key is private and only you have to know it. The private key is something your wallet software uses to sign the transaction that spends your coins. Only the correctly signed transactions will "go through". The private key is nowadays generated from a HD seed (usually 12 or 24 English words). Whoever has the seed or private key can spend the coins.
Now.. you didn't say what kind of wallet you use and this may be part of the confusion. If you use a custodian wallet, then the private key is hidden from you, because actually the custodian owns those coins and you actually only have an account there; the custodian will handle the coins for you (just beware to the risks related to custodians: "not your keys, not your coins")