I don't understand how these types of things are safe when the person who makes them has access to your private keys.
No they don't. Only you have access to your private key, you are the one who assembles the letters in order, not the manufacturer.
One question with that. BTC addresses have checksums. Don't private keys too? How do you do that manually than?
You have a seven step guide here, it's easy:
https://en.bitcoin.it/wiki/Wallet_import_formatThere are also several offline utilities to do it securely, but you should not choose your private key arbitrarily in the first place. You wallet can export the private key in WIF format doing all that work for you.