Translation:My mother is an artist who paints paintings.
No. "Tiu" means "That one", as in "Mi sxatas la pentrajxojn. Tiu estas aparte bona." ("I like the paintings. That one is especially good".) "Kiu", like the English "who", can be a question word but also a pronoun.
Not really. That would be "pentristo kiu pentras pentraĵojn". "Artisto" is any type of artist, whether sculptor, potter, etcher, or whatever.