This is good practice to do. I always check if I can recreate an address before funding a private key that wasn't created by a wallet.
This. It would be like putting a bunch of cash in a safe without first checking that the key works, only the safe is completely indestructible.
The right way to make your own paper wallets it's with vanitygen.
There is little inherent difference between using a website which you have downloaded and ran offline and using a piece of software which you have downloaded and ran offline. Both are equally capable of being filled with bugs which generate incorrect addresses, and both are equally capable of returning fake or pre-generated addresses to which an attacker has access to the private key.