There are no other ways of paying for things than the ones you have listed, watermeadow, except barter (and what if you can't do anything for them.)
If you give people a cheque, they could keep it until they can take it to the bank. You would feel better if you paid up, and presumably they are paying by card so they have no immediate problems.
You say you are terrified of the technology of online banking, but you are coping fine with the technology of joining Gransnet and posting - there is honestly no more technology involved in online banking!
You have a username (as on GN) a password (as on GN) plus a further security check number or word. Signing in usually involves quoting the username and the password and then giving the bits of the security check that you are asked for (first, third a
There is a lot of anxiety about anyone finding out these details and cheating you, but unless you hand them over in a reply to a phone call from a stranger, they are pretty safe. You could keep your password and security check written down and kept somewhere out of sight if you are likely to forget them - just don't choose one of the places that burglars always look first. Actually, a burglar is more likely to take your TV and your laptop or I-pad to the pub and sell them than waste time rifling through your underwear drawer looking for passwords!