Q1.
Some Modifier cards say that "Skip your next draw phase after this card is played".
ex.
I just played this card on one of my character, should I skip the draw phase of "this turn" or "next turn"?
Q2.
If I played "Mystery Tour"(A card in UE expansion) in my first action, I drew three cards and there was an UD, Can I play this UD instead of discard it ?
"Set your hand aside and draw three cards. You must immediately play these on characters you control, if possible. Discard any Events, and any cards you cannot play."
What I want to know is that if I played this card in my 1st or 2nd action, could I play UDs on my characters if there are UDs in these three cards?
Actually, it doesn't matter if it's your first or second action: you can ALWAYS play Untimely Deaths that you draw as a result of Mystery Tour.
The rule on Untimely Deaths is that you cannot play an Untimely Death as your second play. If your second play is the event A Stormy Night, Mystery Tour, or any other card that allows you to draw and/or play additional cards, those additional cards can be Untimely Deaths. You second play wasn't an Untimely Death; it was Mystery Tour, and the CONSEQUENCE of that play is being able to play additional cards.
So what does Mystery Tour mean by "Cards you cannot play"? Exactly that - cards that have specific prerequisites you do not meet. For example, Was Widowed At The Wedding can only be played on a character with the Romance icon. If you don't have such a character, you must discard the modifier.