Yes and yes.
A character is skirmishing if it is assigned to a skirmish that is currently being played (at any given time, only one FP character can be skirmishing and only minions assigned to that character are skirmishing).
A character starts being assigned at some point of assignment phase (either when it's assigned by an Assignment phase action or by standard action) and is assigned all the time until a skirmish this character is involved in resolves. Multiple FP characters can be assigned at the same time.
Example: we have a fellowship including a
Gondorian Ranger with
Ancient Roads in support area (and 3 rangers in fellowship so that its ability works). There are 3 minions on the table:
Dunlending Brigand,
Dunlending Looter,
Dunlending Madman. FP player assigns Brigand to Frodo, Looter to some ring-bound ranger and Madman to some other ring-bound ranger. He then chooses to resolve skirmish involving
Dunlending Looter. During this skirmish:
-
Dunlending Looter is affected both by
Gondorian Ranger and
Ancient Roads (because he is assigned to a ring-bound Man and skirmishing a ranger), his site number is 7 (his own 3 and +4 from cards),
-
Dunlending Madman is affected by
Gondorian Ranger (he is assigned to a ring-bound Man) but not by
Ancient Roads (he is currently skirmishing noone, so he can't be skirmishing a ranger), his site number is 5,
-
Dunlending Brigand is affected neither by
Gondorian Ranger nor by
Ancient Roads (he is assigned to a Hobbit and skirmishing noone), his site number is 3.
So, if FP player plays
Arrows Thick in the Air, all 3 minions will be wounded if the fellowship is at site 2, Looter and Brigand if the fellowship is at site 3 or 4, only Looter if the fellowship is at site 5 or 6, no minion if the fellowship is at site 7 or higher.