Part payments can be made by clients providing the options have been enabled. This can be done on any payment provider. The difference with GoCardless however, is because of the nature of the direct debit system, you can request the funds from within QuickFile (either in whole, or in part), rather than waiting for a client to login and do it.
You can find more about partial payments here:
Allowing clients to make partial payments on invoices
I referenced a link above for the feature request thread for partial payments, which has since been moved to the “Implemented” category (November 2017).
Regarding the card fees, while these aren’t permitted in law for B2C transactions, they are still permitted on B2B transactions.