Taking off or landing a 20 Ton F-35B on a GG or simular carrier would be pretty scary. It might be able to do it, just, in good conditions. However throw in bad weather and I wouldn't be so confident of ops, those carriers are pretty low too. I don't know if the decks could take it either, the F-35B is heavy. Like F-111 heavy.
Nowhere near as heavy as an F-111.
F-4 heavy.
Landing is vertical, relative to the ship. There would be no difference in difficulty landing on Giuseppe Garibaldi or Nimitz. The designated, clear, landing spot would be about the same size. The only difference would be if the weather is heavy enough to throw the ship around.
Deck strength is a potential issue, but isn't a function of the size of the ship. Otherwise, the size & weight is irrelevant when it comes to landing.
Height? Ask the USMC pilots who've flown off them with Harriers how it compares with flying off a 40000 ton Wasp. They say to the press that the ski-jump means that despite the much smaller size of the ship, they never get anywhere near as close to the sea as they do when flying off USN LHAs & LHDs. They're flung up into the air.
You seem to be thinking in CATOBAR terms, not STOVL.