(Now that I re-read this I see I misunderstood some of the questions but I guess they're answered now.) I've been replaying this and found that I hadn't mastered the tactic (of course most important) part of the game. The only game I had the time of patience to finish was the first I ever played. I've quitted, hopefully temporarily, even the game I was playing currently, but before I managed to learn some facts about tactics in the game. Well many people may have figured this out already but I guess I'm bored, so here are two more cents.
The "reactions" stat is not that important, I personally think now that it's one of the least important, far behind shooting accuracy, TUs, etc. It governs only things your soldiers do during the aliens' turn, and you must lead the squad so that the important things happen during your own turn. Don't leave them out in the open or in long non-cleared corridors, go from behind a corner to behind the next one each turn; if you can't avoid it, deploy some smoke in front.
As you can see when you make a soldier watch into an unexplored region, a soldier's line of sight (LOS) is 90 degrees wide. Whenever you encounter an alien during your turn and he's inside your moving soldier's LOS, you get to act first.
No matter how low your reactions are, or how high the alien's, during a given side's turn that side always has priority. After the encounter, once you move further, or fire and the alien survives, or throw a grenade, or move a second man into the alien's LOS, though, the alien gets a chance to act provided you're within his LOS or you have called his attention shooting at him --I leaned to think that he could lose that chance if he failed a reactions check just like it works for you during the aliens' turn, but in my experience he always gets to act. Of course if you move in a way that you come into an alien's LOS without his being into your own LOS, even its being your turn you can't act if you don't see the alien and he'll blast you.
The only things you must keep in mind are the shape of the LOS, and that you must move in a way that nobody can see you without your seeing him beforehand or at the same time. Some examples (yes I know I've got too free time):
Code:
LOS of a man/alien looking north:
**.........
** .......
****.....
**** ...
******@
It's bad to stay right behind a corner. A man (@) is looking north, an alien (A) comes from the east during his own turn:
**** A
****@+----
**** |XXXX
**** |XXXX
Both see each other at the same time, it's the alien's turn, so the alien blasts the human. Looking north-east won't help since the corner prevents the human from seeing more to the east that if he's looking north.
It's best to end the turn one square behind the corner:
**** A
**** +----
****@|XXXX
**** |XXXX
If there's an alien beyond the corner, he won't see the human and therefore won't be able to harm him unless he turns the corner; and if the does the human will get a chance to shoot him provided a reactions check is passed.
When it comes to moving from cover, it's a bad idea to turn corners in the obvious way:
****@**A
****.+----
****.|XXXX
**** |XXXX
If there's an alien behind the corner but not right behind and looking west or north-west or south-west, the human comes into his LOS while the alien is outside the human's LOS --the alien blasts the human. It's the opposite case as the previous one.
The safe way to turn corners:
****@**A
** . +----
**.**|XXXX
**** |XXXX
The human moves north-eastwards and no alien will se him before he sees the alien. Being the human's turn, he gets to act first even if the alien is looking at him.
Of course motion sensors help big time in these situations. Also the LOS extends for 20 squares for both you and the aliens --even if you see the landscape farther away, there could be aliens there and you won't see them. So if you're advancing and see for example a cyberdisc far away, you know that if you shoot at it, it will shoot back even if you hit it --you won't kill it because it takes so many hits to kill. But if you shoot with soldiers who are farther away, or even if you step backwards one single square (until you're 21 squares away of the cyberdisc) and shoot with that same soldier, the cyberdisc won't fire back since it's not seeing you.