If the equipped creature somehow deals combat damage to a player on an opponent's turn, the second ability will trigger. You'll be able to cast cards you exile if timing rules allow (so, instants, mostly), but you won't be able to play a land that turn.

The effect that allows you to play an additional land that turn is cumulative with other effects that do so, including itself. If the second ability triggers multiple times in the same turn, perhaps because there were multiple combats, you will be able to play that many additional lands.

You must follow all normal timing rules for a card you play using Sword of Forge and Frontier's second ability and, if it's a spell, you must pay its costs to cast it.