Rusty chain and back cassette – Replace or repair?
As long as the crank arms, chain and freewheel turn freely and all as one. Without clunk's, slipping or sticking at any point there should be no need to replace any of it. The surface rust will not prevent it being fit for purpose and should wear off with use and some decent lubricant. You could always try a wire brush to remove surface rust without having to disassemble any parts and also just for reference if you do decide to change your "cassette" be advised that is a freewheel and not a cassette they are not interchangeable so avoid disappointment ordering a part that will not fit. The part you would need to order if you decide to is a 7speed freewheel not a 7speed cassette.