After I spend a week in Venice, I want to rent a car and do a road trip around the Dolomites for a week and then drop the car off at VCE on my way out. What would be the smartest way to rent the car? Can this only be done by picking up or dropping off at the airport or are there other, faster non-airport options for picking up the car?
There are car rental offices at/around Piazzale Roma, across the Grand Canal from the train station, and easily reached by vaporetto. That would be the most convenient.
You can then return the car at the airport
I just wanted to add an extra word of warning. Driving in Italy often comes with tickets months later if you drive anything over the posted limit or accidently drive in an exclusion zone. Make sure you spend a little time becoming familiar with these traffic signs.
Yes. In particular, the causeway leading out of Venice is full of speed cameras with a low speed limit (50 or 60 kph, can't remember).