No, you may stay at any hotel you like. Uber is very easy to use in Puerto Vallarta and town is only a 10 min drive from the hotel. A hotel day pass will need to be purchased for $150/person if not staying at the hotel.
We like to use Uber since you know the price before hand and don't have to negotiate with Taxis. Although, Taxis are a great option for quickly catching a ride where ever you go!
Yes, although, every restaurant has a different exchange rate. We recommend going to an ATM and withdrawing pesos. (You can also do this at the airport before passing through Security)