1) How do you handle punctuation with parentheses, particularly with question marks?
The vast majority of the time, the punctuation will go outside the parentheses:
Jen accidentally dropped her cell phone into the toilet (no big loss; she hated her phone anyway).
The comment inside the parentheses is just that: an aside. It's not a sentence in and of itself but part of the larger one. Because of that, you end the big sentence with a period on the outside of the closing parenthesis.
With commas, put them on the outside. There might be a situation where inside is correct, but I can't think of one.
As for question marks inside or outside the parentheses, the answer to that is: it depends.
Ask yourself: Is the inserted (parenthetical) thought a question itself, or is the full sentence the question? That'll tell you where the question mark belongs.
A question mark goes INSIDE if the parenthetical is a question:
Jen accidentally dropped her cell phone into the toilet (didn't she hate that phone anyway?).
If the entire sentence is the question, the question mark goes OUTSIDE:
Didn't Jen say she dropped her cell phone (which she hated anyway)?
2) Can you do parentheses within parentheses?
Sort of, yes. You can definitely have a parenthetical thought inside another one.
But . . . when you do that, it's similar to when you're doing a quote within a quote: you use a different punctuation mark for the second set.
You start with regular parentheses, and then for the second set, use brackets. Be sure to close the brackets before you close the parentheses:
Jen accidentally dropped her cell phone into the toilet (no big loss [she hated the color anyway], but the phone was a gift).
Hope that helps!
Note for picky readers: Yes, I know that there's a misplaced modifier in that last example. I'm too lazy to fix it.
Bragging rights to readers who know what I'm talking about and can identify it!