Yes both valet and self park. The hotel has secure designated carparks available in a nearby parking building at a reasonable rate given it's inner city. On street parking is available for a quick stop but it's a narrow and busy street plenty of demand.
It's not a motel, that's for sure. Street parking is 24hr and heavily wardened and I think you can stay max 2 hrs. There are several very large multi stories nearby, but they aren't cheap.
Yes both valet or self parking
Get an answer from Hotel DeBrett staff and past guests.