Specifically, what do the lightning bolt, fist, lightning bolt, and x2 mean?
The icons inside the circles are the type of enemies that will spawn from that gate. Enemies will take little to no damage from towers of matching symbols. So lightning bolt portals spawn lightning monsters and will take reduced damage from matching towers. The monsters can also have additional mods such as cannot be shocked, or in the case of the fist (physical), cannot be stunned or knocked back.
It may be hard to tell, but the X2 follows a little loot bag symbol and means you will get two chests from that portal upon successful defending it instead of the standard single one. The blighted symbol at the top of that same portal indicates a boss will spawn from there as well, which is why it is giving double rewards.