Starcraft – Does Wings of Liberty have global play on its own

If I'm understanding your question properly, in order to have two Heart of the Swarm licenses you need two Wings of Liberty licenses.

Since Heart of the Swarm is not a stand alone expansion, you need to have all the prerequisite games in order to play it (each copy).

You can see for example, on this Cataclysm box art for World of Warcraft, that it requires "Wrath of the Lich King to play". Wotlk says it requires TBC, and TBC requires the base game. It is expansions all the way down. This trend stands true for all Blizzard games to date, as they don't release stand alone expansions.

In the starcraft 2 lore panels at blizzcon 2010 and 2011 they answered these questions. The canonical choices are the A choices, so

Raynor chose Tosh over Nova

Raynor chose Dr. Hanson over Selendis

Raynor chose the Tunnels in Belly of the Beast, not the platforms in Shatter the Sky

transcript for the first two.

Best I can find for the tunnels answer is the entire lore panel from 2011.