You can install it on as many systems as you own. Also Actually While i don't know the rule particular to elemental i know for sins of a solar empire your allowed to have a friend play with you online if its for the intent of YOU playing together not piracy.

Excellent.

I'm SP only..  So will be fine.

This game does not have copy protection, so you can play it on two computers at the same time (it may be against EULA, but there is nothing that actually can check if you are running it or not)

There is simple way to test it. First fill your bathtub with water. Now place your computer in it.

Did your computer float? If yes then that probably wasn't your computer, try again.

Okay did your computer sink? This is a clear sign that you can't run elemental, because some idiot ruined your computer by submerging it in water.

Seriously though, you can install and play elemental on all your computers with no hassles. The game should run fine, but you may need to lower some of the display settings and tolerate some slowness on older machines. But it's a turn based game so it's not like that will cost you the game or anything.

I'll be testing this theory as soon as we can download the game. (I have a regular gaming desktop, so I didn't buy it solely for this reason )