I would have accepted either Bank Club Reno or Reno Club.

2.) First worldwide broadcast from Nevada.

From Kling:

The Tavern featured The Tavern Music Makers for its patrons and dancing and listening pleasure. Heading up the restaurant was Chef Jean Sigg, formerly of the Willows and The Club Cal-Neva at Lake Tahoe. The club gained national attentions for the fine cuisine and lavish appointments. Famous entertainers such as Lionel Hampton and Nick Stuart appeared at The Tavern, and nightly radio broadcasts originated there. In fact, The Tavern constructed it's own broadcast control room to eliminate the difficulties of remote broadcasting. The first worldwide broadcast from Nevada originated from The Tavern in 1935.

2.) Ranks remaining open

3

Mark