here is my question

1. If you have no cards in hand, at the start of your turn do you have to draw and discard? Or would the Mask do nothing and then you draw your card for the turn?

2. If you have one card in your hand, can you choose to draw first and then choose which to discard?

thanks to all who try to help me with this question

No to both.

All "start of turn" effects go on the chain before you draw a card. They are resolved and a Priority window opens - this is where u can play instants, complete quests, etc. When the chain is empty and both players pass, the active player draws a card, then the Action phase begins.

What you can do, if for example u have a quest face up and 1 card in hand which u don't want to discard, you can complete the quest in response to the Mask effect, then discard the least desirable card