The manual basically just tells you to fire your gun as a makeshift look key: "RMB in direction and LMB."

So many things this first iteration does so terribly wrong. I've been tempted to skip to the second more than a few times, hoping the sequel learned a few things, first of all, that cover is arbitrary and hard to judge, but I've developed a reasonable intuition for it enough to gauge almost exactly how much cover my guys and the bad guys have unless there is a cluster of trees and bushes (what a clusterfuck).

The manual should say "Hold RMB at square you want to look, then LMB."

So basically, all move but the opposite.

Is there actually a question there?

No? O.o

I think "l" or "k" is used to turn in the second game. Don't know if it's the same in the first game.

If you don't enjoy the first game, I'd recommend you skip to the second one. No need to finish the first one. The story is different (the only continuity between the 2 games is that you have mercs from the first ported into the second), and the game is really better. Better UI and controls, too.

There is a button with 2 arrow circling each other that permit the selected character to turn around and look, pressing it a second time in the same direction make the character raise his/her weapon

You'll need to enter the detailed ui section by right clicking on that specific character to see it

VERY late, but incase someone else has this issue.

I found out that if you HOLD right mouse button (instead of just tapping to aim your gun.) then tap left you'll look in a direction.

Couldn't find this in the manual.