There is no civilian death limit in 2.2.1 (unreleased at the time of this writing) and later. They hurt your faction standings (which will lose the game if low enough), but nothing more. Aliens also use reactionfire in 2.3 (not sure about 2.2.1) so you should get used to that, because it'll happen soon.
I see you have nanocomposite but no weapon research. Never rely on armour for anything, best defense against an alien is putting a bullet in it's head. My current tactics revolve around getting laser rifle as fast as possible, until then I rely on basically heavy weapons and explosives. With laser rifles I then quickly switch to assault as primary.
Also take into account it's normal for you to still have a couple of casualties on some of the harder missions.
Basic survival rules are:
1) Always cover all flanks, it's no fun to take silent casualties due to backstabbing aliens with kerrblades
2) Never leave your guys out in the open, a stray particle beam can destroy your poor soldiers
3) Use a lot of coverfire and play conservatively unless you have a reason not to like 50 assault weapons skill, laser rifle and nanocomposite
4) Crouching increases accuracy - go for the preemptive headshot / rocket blast for easy first turn kills
5) Make cornered aliens come to you, don't go to them. Even though the last tamaan is probably panicked, he can still one-hit you with a kerrblade. Covering with sniper/machine gun and flushing out with grenades/flamethrower is a good way to get them out.
The more you play the more you'll see how aliens behave in different maps, allowing you to exploit their weaknesses. Example would be a crashed harvester. Camp the area around the fire with machine guns and sniper rifles. Flush the second floor with grenades. The aliens will eventually all come out and just get destroyed by reaction fire. The few hiding on the top floor will succumb to the grenades.
Another interesting map is the military convoy, if you end up hiding, popping out, shooting the aliens and hiding again in the same turn, you'll destroy them. You need good accuracy, laser weaponry works best.
Damn... long post. You can tell I play too much...