Does the free copy of Starcraft 2 on the battle.net launcher have all the campaigns from all the expansions and heroes?
According to http://us.battle.net/sc2/en/blog/21173629/starcraft-ii-going-free-to-play-explained-11-3-2017 (top hit on google btw)
you can now play all of StarCraft II’s multiplayer, every Co-op Commander, and the entire first campaign in the single-player story, for free
Or in more detail:
The original Wings of Liberty campaign. Experience the original epic campaign that kicked off the StarCraft II saga! If you picked up Wings of Liberty previously but haven’t come back to StarCraft II in a while, we’ve got good news for you too—if you purchased Wings of Liberty prior to October 31, 2017, you’ll receive the second installment in StarCraft II’s campaign, the zerg-focused Heart of the Swarm, as a limited time offer from November 8 to December 8. Make sure to log in during that window to claim it!
You will be able to access the ranked multiplayer ladder to compete with other players to become the best of the best, complete with all of the multiplayer units from Wings of Liberty, Heart of the Swarm, and Legacy of the Void. All you have to do to unlock it permanently is earn 10 First Wins of the Day in Unranked or Versus A.I. play—our way to preserve the quality and integrity of the ranked experience.
Current and upcoming Co-op Commanders are available to play for free up to level five, and the level restriction for weekly mutations has been removed. You’ll be able to tackle these extra challenging missions with your friends right away. The Co-op Commanders Raynor, Kerrigan, and Artanis will remain completely free, meaning that you can keep leveling them to your heart’s content.