Yes, the vans fit in the covered parking structures. There is also street parking as you go to the lot where you can park, as well as a smaller lot ground level behind the piazza.
Rates for the lot are:
€ 2,00 first hour, cannot be divided into fractions;
€ 2,00 from the second hour, can be divided every 30 minutes.
Daily fee: € 10,00 the first day, € 15,00 second day and € 20,00 from 3rd day forward. They surely don't encourage long term parking there!