Re the BACS thing. I’ve always called any bank transfer BACS much as I call why suction based cleaning device a hoover.
I think very much this, all our business stuff ask for bacs payments but its just an electronic payment, faster/chaps or what ever. If they’ve given you the sort code/account number just crack on via your personnel account.
In regards settlement, when i’ve seen settlement offers from finance firms (i’m in the insurance game, receive them relatively often after total loss claims) they just have the total owed, never seen one with calculations. You’ll need to press for that but should be able to work out from your contract.