So lets say I had the keys on my Ledger nano S, and as a precaution I wrote them down.
I loose the Ledger nano ,but still have the private keys written down.
Am I still able to cash in the BC without the Ledger?
Yes, you still can. But I just want to emphasize that more than the private keys, you are writing down your 24-word seed phrase. Your seed holds all your private keys and addresses. That's the key to all your cryptocurrencies. Whether your Ledger Nano is lost, destroyed, or stolen, you still have your cryptocurrencies with you safe and intact.
Next question....
When an exchange sells me BC ,and I get my private key , does the exchange ever see the private key they send me ?
I don't mean if I leave the BC in trust with an exchange or whatever .I mean if I posses the private key and it's on my ledger wallet !
No, they don't know your private keys. By the word itself, it means the keys are private. Even if exchanges or anybody for that matter send you Bitcoin, they know nothing about your private keys. It is yours and yours alone if your wallet is a hardware wallet, unless you willingly share them which you should never ever do.