Cold wallets are stored offline using devices like a Ledger Nano. A hot wallet could be a wallet on an exchange like Coinbase.

All wallets will display your specific keys to that wallet only once, and it is your responsibility to write it down somewhere that it is safe. This way, no one can log into your wallet without your keys unless they have your username and password for hot wallets that is. Cold wallets can't be accessed at all.

Essentially, if your cryptocurrencies are stored on a wallet, you will lose access to the cryptocurrencies if you lose your keys or login information. Wallets are always recommended to use two factor authentication when logging in for security purposes

Setting up a wallet for a specific cryptocurrency is usually as easy as searching which exchanges or wallets that specific cryptocurrency is available on.

Newer cryptocurrencies are sometimes harder to find a wallet for

I try to only send my cryptocurrencies to exchanges if I am planning to sell or use them to buy other cryptocurrencies on that particular exchange.