Yes they do.

Sheraton and courtyard are adjacent to the arena.

The official lot adjacent to the arena costs $35 flat or at the street with official ticket for $10. I took latter as when the game was over we just walked and drove off easily.

No not even water.

Doors open 90 minutes before tipoff according to Chesapeake Arena's Website.

Looking at the ticket prices for the NBA Thunder, this is in the range of the going rate for the lower bowl. I saw some tickets in the $220 range (non resale) for the top row seats in the lower bowl. The lower bowl has nicer more comfortable seating and in the 2nd row of the premier sideline, you will have a close-up view.

You can park on the downtown streets. After 5 p.m., there is no charge for spaces with parking meters. There are also parking lots which usually charge $5.00 - $10.00.

Marriott Courtyard is next door to the Chesapeake Arena. I've stayed there..rooms are clean..parking is $$. Many other hotels 2 blocks away. And many less expensive hotels outside Downtown but don't be fooled....traffic and parking prior to events gets congested. Many one-way streets around arena area. We took a cab to The Eagles concert in May, 2015...expensive but worth it!