So if you wanted to give money to another individual (not a company which offers card payments) and you didn't want to use the internet, is cash the only option?

You call your bank, or go into a branch, and transfer it to their bank account.

You fill-in in a bank transfer form and mail it to your bank (if you don't carry it in person to a branch office). The money gets transferred from the account of the receiver to the account of the recipient within a day. That's a standardized service every bank has to offer in the SEPA area and the price must be same regardless where the recipient's account is. No difference whether business or individual on either end. You need to know the recipient's account number (IBAN). Of course banks prefer that customers use the internet to initiate such transfer, but other methods exist (often at a higher price).

Frankly, this sounds like a long-winded way of saying "you write a check," with a technical difference being that the transaction is a push from the sender rather than a pull from the recipient. If this form has an option for recurring on a (e.g.) monthly basis, then it's what Mullvad could suggest subscribers switch to, if both parties have a SEPA presence.

Yes, monthly SEPA payments (with a static amount and static reference/message) are a commonly used service at least in Finland, for e.g. paying rent between private individuals, and it works as-is with Mullvad wire transfers.