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I believe there was originally a line of dialogue about there being resistance when they pushed through objects, which was supposed to explain why they don't just fall. That line was cut, but IIRC it is still referenced indirectly when Geordi's hand gets zapped and he says that there was more resistance to pushing through stuff afterwards.
That wouldn't explain why there is enough resistance in the floor to stand and walk, but not enough resistance in walls to prevent them from easily passing through. Presumably their mass and the pull of gravity are unchanged, so the resistance would have to be enough to counteract their weight. And even if they did weigh less, they still propel themselves forward through walls by pushing off the floor, so either the floor needs to be more solid, or they should be nearly weightless and move by paddling their feet through the floor until they build up momentum enough to smash through a wall. Also, if they are applying pressure to objects they pass through, shouldn't people they touch feel it?
Personally, I'd probably explain the floors specifically being impassable by blaming it on the way the artificial gravity is generated.
I don't have a good explanation for how they can breathe, how they see without interacting with light, how they can hear clearly when matter isn't really touching them and therefore can't conduct sound, etc.
I don't have a good explanation for how they can breathe, how they see without interacting with light, how they can hear clearly when matter isn't really touching them and therefore can't conduct sound, etc.
That is obviously due to a phase shift in the quantum fields, which is correlated to the mass of the interacting matter (through the Higgs field). This leaves you interacting with light stuff like air and light, but prevents you from interacting with solid stuff like walls (and potentially force fields, if that would fit the episode).
Of course, artificial gravity affects the mentioned phase shift by bending spacetime.
And now I must go, before my handwaving creates enough energy to form a black hole.
Your technobabble is on point, you should be in the writers' room!
Then how come other people can't see them?
They can't? I should watch that series again... Anyway, good point, but of course they can't, because the phaseshift forces truly massless particles (like photons) into a state of quantum entanglement.
That means photons hitting them, create an entangled twin that only exists long enough for them so see their surrounding. The "original" photon however just passes through making them invisible to others. Energy from the surrounding is used to create the twin, cooling the surrounding shortly. However, since the twin is immediately reabsorbed (and the entanglement broken), you basically can't detect the effect.