Why is "Are you painting THE house?" wrong, if we didn't have either "egy" or "a" in the original sentence?
Because a is required, but egy is not. If there's no article, it's "a house".
(Also "the house" would need a different conjugation: A házat fested.)
Thanks, this is very helpful!
I personally feel no article is always a bit more indefinite than indefinite article itself.
How wrong or right would "egy házat festesz" be?
"Házat festesz", "Festesz egy házat", "Egy házat festesz" are all correct. Report it.
Is "Do you paint a house." correct or wrong?
This is very correct.
Again, why isn't the simple present accepted here as well?
Because it is a question . . .. Paint you a house? Well, okay: Do you paint a house?
I can’t recall. Is that painting as in applying paint or including in a two-dimensional work of art?
It's about making a piece of art. As far as I know, it can be either making a painting of a house, or making a painting on the house. Applying paint simply to recolour it would rather be mázol.