Hoo Boy. I'm guessing your house is pretty old, especially since it has aluminum wiring in it.
I just replaced our washer & dryer and here's what I have observed in my townhouse (built in 2000): Our laundry room has two outlets, one is GFCI other other is not. They are both on the same circuit. The outlet for the washer/dryer is not the GFCI (it's on the same wall as the water supply & washer drain). I would have to take the panel cover off to determine how many amps the circuit is but I'm thinking it's 20A. I had to operate both units off of the GFCI (because my wife had to run a load of chair covers - she runs an event planning business) and had no trouble. I think the GFCI is intended for an iron.
As for some of your Qs: Grounding the outlets to the box or conduit is perfectly fine. If there is no ground wire, this is a safe way to get electricity back to the panel (which is grounded).
1) If you run the washer/dryer while running the compressor, you may pop the breaker. It might be better to move the compressor to another outlet.
2) I think you are probably safe in assuming that the piggy-back garage outlet was installed by a p.o. I would change the receptacle to 20A. Or, remove that outlet altogether if it doesn't inconvenience you too much.
3) Based on more recent construction (my house), no, the washer does not need a GFCI.
There are some simple thruths......and dogs know what they are - Joseph Duemer
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