Do you need to be wearing *some* armor, or will it work if you (grand)master the skill without actually wearing the armor?

Perhaps this might justify wearing armor, but not justify wearing powerful armor that's more expensive to repair. On the other hand, this is still only likely to be particularly useful if either:
1. One can get such armor skill on everyone, or
2. There's a way to force enemies to aim their attacks primarily at the characters who are wearing heavier armor. (The lack of a way to do this is one flaw in MM3-5; I've also encountered this issue in the SaGa 3 remake, even though that's a completely different game.)

Armor Skill applies only to 1 equipment slot (body slot). if you wear plate, you get skill bonus from Plate Armor Skill, If you wear nothing, you get nothing in MM6. In MM7+ there is Dodging Skill, which is active if you have no body armor (or if you wear Leather Armor and Grandmaster in Dodging Skill).

If you have no specific armor Skill (Leather, Chain, Plate), you can't wear that kind of body equipment. If your Skill Level is slow, then you also face speed penalty, you get longer recovery times. At high Skill Levels you get no speed penalty for wearing armor.

What concerns second point. The character who is closest to the left has highest chances to be attacked. The character who is closest to the right has lowest chances to be attacked. That works in MM6, this is my observation, I don't say it is 100% so, but it seems to work like that..

MM7+ reintroduced racial/class hatred, and it hurts. For example, all Goblins hate Dwarves., all Titans hate Females, etc.so the hated people get focus-attacked and killed very fast, which I don't think is fair and it is totally unfair when you have low level party.

On the other hand, there is one dungeon late in World of Xeen where that can be used to your advantage. In the Southern Sphinx, you can focus on improving just your Cleric's AC, giving them all the obsidian equipment you find, and also using a fountain to boost it even further, not to mention level boosted Bless, and get the enemies to miss most of the time. You still need to save frequently, as most != all, and a single hit will break all that obsidian gear (and money is in short supply at this point because of training costs), but things should be manageable. Also, it is not worth doing this unless you can get your Cleric's AC to something like 250.

(That is the only place, this late in the game, that AC is meaningful, as everywhere else you're dealing with enemies that don't do Physical damage, and whose attacks are unaffected by AC as a result.)

The hatred for the Dwarf Cleric seems to be a theme in the game,. But I give him/her a high endurance to start and let him take hits while the other three take out the Goblins.
When the Goblin Army shows up, that would be problem if the shot arrows. But they don't so my Cleric can breath a sigh of relief.

Traps works on a different mechanism than hitting in M&M 6 and beyond.
1) Perception works to help reduce or eliminate damage take.(you can tell this worked when you see them dodge in their character screen to one side)
2) Luck will work hand in hand with perception to help avoid damage.
3) Damage can be reduced by the appropriate elemental damage reduction.

So, in other words, armor has no effect on trap damage (unless it happens to have an affix that alters a stat that does matter), right?

To the best of my knowledge that is correct.
Perception is often an overlooked skill. When it is high enough items where you can click for a secret will glow red, like hidden treasures or doors. The higher your perception the lower the trap damage is.