Can max get more money from his parents?
Max already gave Julian 4 out of the 5 crowns he owes him (he gave him all the money he had left!).
He can get more by borrowing against his trust fund (which is based in Nuln) at the merchants' guild. He has a ring with his family crest on that he can use to prove his identity, plus obviously he can sign things and tell them his father's name. He'll do that as soon as he's well enough.
Max's father has provided generously for his son... not because he loves him, but because it would be shameful if his son didn't have enough money to at least look respectable.