Starcraft – When does first win of the day bonus reset

Guest pass answer for July 2010

When StarCraft 2 was released in July 2010 this was the correct answer:

The guest pass allows a guest to play StarCraft 2 for 7 hours of game time or 14 days from activation (whichever comes first).

Once over a retail version can be purchased.

Guest pass answer for August 2011

As pointed out by marco-fiset things have changed since that time. Now the guest pass gives you access to a "Starter Edition" of Starcraft 2 which gives you the following restrictions:

• The first four missions of the StarCraft II: Wings of Liberty single-player campaign, including Mar Sara 1-3 and the choice to embark on Tychus’s first mission or Dr. Hansen’s first mission.
• The first two Challenges: Tactical Command and Covert Ops.
• Access to the terran race in Custom Games and Single-Player vs. AI.
• Access to the following custom maps (map selection may rotate over time):
  • Xel’Naga Caverns
  • Shattered Temple
  • Discord IV
  • High Orbit
• No map editor.

All campaign progress and earned achievements are saved once you purchase the full edition of the game.

The 7 hour or 14 days time restriction does not apply anymore.

I believe you're talking about the Mercenary building. As you surmised, the # displayed indicates how many more times you can hire that band of mercs.

It resets every map.