does этого come from the fact that its accusative form?
Yes. Also that animate masculine nouns borrow from the genitive to form the accusative.
Почему "Ты знаешь этого артиста?" не правильное?
Perhaps because we haven't learned that word yet. XD
It looks good to me, IAmTheSenate; I'd report it.
Why it cannot be 'этот' художника?
because Художника is the genitive form of the word. This is because it is a masculine animate noun and masculine animate nouns take the genitive form when they are accusative. Thus этот must be conjugated into the genitive form too.
Are the accusative and genetive forms for masculine nouns the same?
If they're animated. If they're things (inanimate), accusative looks like nominative instead
The formal/unacquainted version of this be "вы знаете", right?
Yes. You can also say "Знаете ли вы..." ("Знаешь ли ты...").
Художник is specifically a painter, not any artist. Duolingo should not be using this word when they have a better word to translate the english "artist" - артист.
Ты знаешь эту художницу? -- One needs to use Эту instead of Этого here because Художница is a female form of a male noun Художник.
m: Ты знаешь этого художника?
f: Ты знаешь эту художницу?
I do not have russian keyboard