Fun topic, I'll 🤓
First you mention:
Either all wads or no pwads are canon. If our dark lord and savior Romero is to be believed, all wads are canon. Thus all answers can be correct. That said, I tend to base my headcanon on the iwads and treat pwads as fair interpretation, also canonical events.
Are generals warlords? If you're asking merely if they (smm and siegecow) are in leadership positions, then yes, I believe doom 1 explicitly states that. But I guess hell is as much ancient China as it is modern US (or insert your preferred country here, they all fit). Even companies have leadership that controls land. Hell is a society of some sort and has a hierarchical structure, but idk that comparisons to real world nations/groups is without its issues.
I would say yes, the one we kill in doom 2 is in a different location to the one in plu and the one in tnt, and icons cant move. Another good question would be if it is more of an object than a creature if we consider parallels to narrow ai 🤔🤓 although I suppose the differentiating criteria of "it doesn't move" is fairly flimsy and that would also open the question to the rest of the roster, and perhaps doomguy himself. Maybe the icon is just a vessel for the overarching leader of hell to act through from afar, like how sauron leads his armies in lotr.
This is a big question on its own and your paragraph asks a thousand more. It's a hard group to answer... I suppose in the first place, it's arguable if a hell leader even exists. Maybe some lucifer-esk entity exists somewhere and acts as sauron, from afar, but the concept/setting of hell itself is also presented as much of a character as doomguy. The messages at the end of the episodes don't read "the moodemon/smm/lucifer/icon/healer/etc" didn't play fair, it says "hell didn't play fair." Hell in this sense is perhaps more a force of nature than an entity, or maybe some cosmic cthulu mythos being shaping its dimension to its whim, but probably just a force of nature. Perhaps the very nature of the dimension itself, naturally bleeding over where it finds gaps to fit through. Who knows lol.
I do think doomguy died at the end of e1m8, which would point towards the new dimension being actually hell, though I don't consider it to be a christian hell. More like a general hell.
Doom describes the demons as interdimensional, but that doesn't mean they come from the only other dimension around. There could be other dimensions, it just so happened that teleporting technology uncovered this one, which also coincidentally seems to be where souls of bad humans go, at least if we take the in-game lore at face value. It could be argued that humans in-lore just mistakenly interpreted the new dimension as hell, being the closest comparison they knew, or maybe the entity/nature behind hell just shapes itself to its victims' fears.
Presumably to amass more soldiers and a larger area of influence. The age old "number go up" motivation 😋 Or maybe they just want into our dimension so bad that they've been waiting for such an opportunity. Alternatively, maybe it's just the nature of the dimension to corrupt and expand. Maybe the fighting is not because of hell doing its natural thing, but because of our desire to fight change, in this case to not become hellspawn. Maybe being a hellspawn wouldn't be so bad 😋