Why didn't he fall through the floor?

The general consensus is that he was trying too hard with doors and moving objects. He didn't have trouble with floors and chairs because walking and sitting is instinctive, so he never doubted that he could.

This is basically explained in the movie itself, during the Subway Ghost's speech:

"The problem with you is you still think you're real. You think you're wearing those clothes? You think you're crouched on that floor? Bull****! You ain't got a body no more, son! [taps head] It's all up here now."

In other words, Sam isn't physically there. His entire appearance that we see--his wearing the shirt and pants he was killed in--is nothing more than his own mental projection of himself. He looks the way he expects himself to look, and he's subject to the rules he expects to be subject to. He doesn't fall through the floor because he doesn't expect to fall through the floor. He isn't subject to the laws of gravity, but he is subject to his expectations of the laws of gravity.

The only remaining question, then, is why he moves through objects he attempts to move--doors, lamps, soda cans, and so on. Wouldn't the objects simply stop him in his path, the way the floor keeps him grounded? Of course the movie is simply following the common conventions about the way ghosts experience the world, but if you want an in-universe explanation, I suppose the answer is that his attempt at conscious control over the objects is what stymies him. He tries to move an object, but he can't, and he experiences this limitation as his hand passing through the object. But when he stands on a floor, he isn't trying to move the floor; he's simply experiencing reality the way he was used to when he was alive.

Another way to look at it is he is simply floating around. Lol. He doesn't walk, he hovers in style.

They should have just made him appear in a white sheet with holes for his eyes and float 2 to 4 feet off the ground to avoid all these questions of logic. No one would have questioned that.

I think it's the grandfather effect

When we were little trying to walk we never fell through the floor.

Hence that's probably why.

Why did he dodge the poles on the subway train as he was walking through?
When he leaves the bank with Whoopi G, it seems as if she instinctively moves her body around Swayze, obviously he is really there, so she is reacting to his physical presence, but in the films context she can't see him, so she wouldn't know exactly where he is. I need to re-watch that though to see if I just imagined it.

How did he get that penny to slide from the floor to door without it going back under the gap? A human could lick their finger so the penny sticks to it, but not a ghost.

Well, he is a spirit and has no mass. Thus gravity would not affect him. So he ain’t going to fall through a floor though he could pass through it.