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For the first question. How do i enter the mask party?. You need to wear a tuxedo set (from tuxedo pant, tuxedo suit, black dress shoes, black socks and frilled white gloves) if you're playing as a girl then sorry i can't help you. The most important thing is the mask, which you can buy in peacock's feather (from the entrance of upper new ark city go to the left, when you see a place name hospital, go up and then you'll see the peacock's feather place) just choose one of the mask and you're ready to go.

Note: everything you need for the mask party can be bought at peacock's feather and the rule of the party is don't ever wear your mask off. Otherwise you'll be stripped naked and tied onto the wall

For the second question how do i complete the mansion maid challenge?

Well, all you need to do is to ask rinny to accompany you to the mansion. When you want to talk to the maid rinny will take her leave (that doesn't mean she'll back to her house. She'll just go to talk with pixie). Talk to the maid and do her challenge. Now, instead of you bumping with pixie ( a purple succubus in robe. Sorry if i'm wrong.), Who'll eventually get suspicious with you, you'll bump into rinny, who you can bluff your way out and there you have it.