Yes! There is a garage attached to the venue. The entrance to the garage is on 6th street.
There is parking at the hotel for your convenience, but it is pricey. (I think 45 a day) But there are other parking lots downtown that should have much better rates. Street parking can work too, for a cheaper option, just make sure you read the signs and pay the meter! I'm sure you have seen "Parking Wars"!
NO!! In fact, we encourage our guests to either: walk! It's a really nice area and fun 5-6 block walk to the venue. take a short ride on the eastbound subway (its right outside your hotel) to 5th street (less than a block from the wedding!) get an uber! (it should be 3-5 bucks, max!)