Can I connect a M4 Mac Studio to a late 2013 Mac Pro via ethernet for file sharing?

if you are connecting DIRECTLY, and not to your Router in each case, you will need to have the speeds match.

The Mac Studio does not do 100 Gbit/sec Ethernet, minimum 1000.

If you place your Router in between, any speed and settings differences will be resolved automatically. Be sure to use "real" Ethernet cables with all four pairs of wires present and connected correctly.

Yes, of course. Macs are strongly compatible across hugely different versions on MacOS, and can talk to other systems as well.

Why do you hesitate?