Is compacted hardcore on earth a solid base for a shed or car parking?

Yes if the hardcore is blinded with sand and gravel, viberated then slabs laid flat and even on top, this is for the shed, For car thats ok as it is as long as it dont break your ankles when you walk on it.

I usually compact hardcore in 150mm to 300mm lifts depending on its makeup. It's essential to have a fair mixture of fines and soilds so that it binds together well. I would always finish off with at least 75mm of MOT Type 1 sloped at 2˚ for drainage.