I have one of these ( picked up a while (long while) back from a boot sale- still needs new feet and a dodgy lead out cable re-soldering, on the to do list!).
The small potentiometers (or 'pots') , that are the speed controls will need a clean, I use Servisol switch/contact cleaner, but any brand should do, from memory I think you will need to remove the base to gain access, so unplug the deck, then a little 'squirt' of cleaner, you need to get it right inside the pots, then turn them back and forth a few times.
The deck should be placed on something solid, the original rubber feet offered some isolation, but not much, so solid and isolated (with spikes, maybe) would be best. Obviously also depends a bit on floor type, concrete, suspended wood etc.
As for replacement feet, this ties in a bit with the above on placement, you might try and get hold of something similar to the originals, or if it's used on a isolated stand/platform you could use just about anything, depending if you want to DIY or buy, wooden/metal cones, dowel rod, rubber blocks etc. I once supported a deck on black plastic 35mm film canisters (there still around -- just!), it was a temporary measure, whilst I fixed it, but they looked (and worked) ok!
The cartridge is a bit of a try it and see thing really, some older carts go and on, but yes the rubber can/will stiffen over time. New carts, budget end the Audio Technica 95 or 120, going upwards the Ortofon 2M Red might be worth a look. Plenty more options available.