is a ledger nano s wallet safer compared to a paper wallet that i just write down all the codes or email them to myself?
Both can be equally safer (unless you email them to yourself, in this case, your wallet security is compromised). The big advantage of hardware wallets is that you can use it on a daily basis while not losing any security. For paper wallets, you need to import your private-key somewhere to spend the coins. If you do this in an infected computer, your coins can be stolen.
what is you lose your nano s device? does that mean all my crypto on that device are also gone?
That's what the backup seed is for. If you lose your device, simply buy a new one and restore your wallet or restore it outside the hardware device in a desktop wallet (in this case, the wallet security may be compromised).
does nano s store the 0x coins? if not, where do i store my 0x coin at?
Yes.
can i safely use my nano s device to log in using a public library computer? (i do not have my own desktop and use library computers)
Yes. That's the main advantage of the hardware wallets (you can even use it in an infected computer).
what do you think of 0x? is 0x going to be valuable some day or not?
Probably not.