Does everybody in USA live in houses like palace?

No.

I might be wrong, but I believe they use that cliché so much because it makes things easy: Larger sets, no one worrying about losing money when they're not able to go to work, easier to flee to a large hotel room if they have to leave the house, etc.
Same as in real life: Money makes a lot of things easier :)

I wonder about that too. And often both parents are working with a kid/s and a dog, so I wonder how do they maintain and clean that house?

Quite the opposite in major cities. I live in NY. You pay a lot to live in a small house. Go elsewhere and you get 3 times the size house for less money.

No way at least no one I know lives in a house that’s like a palace.

I do.

Yeah a lot of people do, too many, IMO. Its a sign you've made it, getting that big house up on the hill...and its never made much sense to me. Its the American dream, but even if I could afford it, I don't think I'd live like that. Big house means a lot more to care for and clean, a longer walk to the kitchen for a midnight snack, more "stuff" to need to fill it with.
Less is more when it comes to homes, IMO, unless you're going for a big family with a bunch of kids. Nothing worse than a big family being packed into a tiny house, really =D