OK, that's a freewheel, not a cassette, and the rust isn't an issue.
Remove the wheel, and if the freewheel spins backward with a nice watch-like clicking it's fine, though you might want to wick a few drops into the gap between the inner and outer body.
If it isn't smooth, sounds gritty or doesn't engage positively it can usually be saved with a good solvent flush and relube. This should be done off the bike so you'll need the correct freewheel remover. If you've never removed a freewheel get advice or read a tutorial because while it's easy, it requires lots of torque and it's easy to damage the freewheel or the remover.
The chain may be OK, and come back to life with some good chain oil. It's a judgment call as to how much rust is OK before the chain is dangerously weak, but older chains had thicker plates and therefore deeper reserves. If you're in doubt, or expect to ride steep hills, replace it, they're cheap enough. If you only expect easy riding in the flats or near the shore, you can keep it on safely.
__________________
FB
Chain-L site
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