I have the free version of StarCraft II (the one from Battle.net). Can I play StarCraft II with a friend — us against AI? How? His computer will be in the same network (IP) as mine.
When both of you only have the free edition, you can:
- play co-op with free (Raynor, Artanis and Kerrigan) commanders
- play arcade contents (they are inherently free)
- play elimination; elimination is now free
- play Wings of Liberty (Terran) campaign
As long as your friend has LotV, you can play co-op with LotV (Swann, Vorazun, Karax, Zagara) commanders as long as you are in the same party with your friends. (FYI this does not require you to be in the same network with the friend; Battle.net provides the means to make a party with a remote friend)
Regardless of what the party member has, you can’t:
- play campaigns not purchased (Heart of the Swarm-Zerg, Legacy of the Void-Protoss and Epilogue, Nova Covert Ops-Terran espionage)
- play with premium co-op commanders not listed above (they can be leveled up to level 5, but they are rather thought of as “starter editions”)
Yes, you can play with your friends who bought the game ages ago.
The base game itself became free some years ago. Since then, it's like you bought the game "Starcraft II: Wings of Liberty".
Upon account creation, StarCraft II includes the following:
- The complete Wings of Liberty campaign
- Full use of Raynor, Kerrigan, and Artanis Co-Op Commanders, with all others available for free up to level five
- Full access to custom games, including all races, AI difficulties, and maps
- Unranked multiplayer, with access to Ranked granted after the first 10 wins of the day in Unranked or Versus A.I
Once you reach level 10 with a Commander, level 15 with a race, or make any purchase, you can also access public chat channels, and join or create Clans and Groups. Making any purchase also grants the ability to publish custom maps.
See also this blizzard post from 2 years ago.
As described, this includes custom games and unranked/ranked(after 10 unranked) games. It doesn't matter if your friend is in the same LAN or anywhere else as SC2 does not support local-only multiplayer. You need a internet connection to join/make games.
Also, as far as I know you can play content from the expansions (Heart of the swarm and Legacy of the void) if your friend owns them .