Let's say I have Well-Crafted Armor, and I exert a dwarf wearing it to play a condition. Does that exertion count as a wound for the purposes of placing tokens?
Yes, GE is right. When placing wounds, they can be 1 of 2 things: either a wound, or an exertion. Once the wound is placed, it is a wound regardless of its source, but when it is being placed as an exertion, effects which trigger off wounds do not trigger and vice versa.
Also, what is the sequence of events with skirmishes? Who gets to play events first? If the Shadow player has Orkish Invader, can he use that right away before the Fellowship player can prevent him using that text with some event?
Yes, FP player always gets the first action in each phase (so in each skirmish, the FP player has a chance to play an event or use an ability before the Shadow players get a look in. HOWEVER, the case you sited with
Orkish Invader is a different case, because the action triggers at the START of the skirmish phase. This happens before ANYONE plays skirmish events or skirmish actions. If more than one "at the start of skirmish" actions happen at once, the order is as follows:
1) Mandatory actions (like
Rider's Mount)
2) Optional actions (something with "you may" like
Orkish Invader)
Where there are multiple mandatory or multiple optional actions due to happen at the same time, the Free Peoples player decides the order in which they happen.
Thranduil