Does Robot remember his life prior to Annie rebuilding him?
Yes he does.
Maybe! Remember guys, I won't answer plot stuff directly.
What inspired robots appearance? The wings (and such) that is?
Had Robot ever existed as a full robot before (with body and everything) before Annie put him together?
Yeah, Annie just put him back together and turned him back on when she found him.
Is there a reason Robot's body got taken apart the first time?
We've seen from the dog-trees that the shadow people can control trees. When Robot returned with the tree arm and the shadow man, was the shadow man controlling him through the tree arm?
Partly, yes. 
Did Kat design Robot's new body along the lines of Diego's old robots, or did she make him more like the newer generations of robots?
He's more like the current generation of robots, and his body is basically made up from spare parts again. 
Will Robot ever get a unique name, or does he like being called Robot?
He's just robot for now 
On his return from the forest, do robot's missing wings have any significance?
You could see it as a loss of innocence, if you wanted to quantify it in such a way. Otherwise it's a hint that something is not right, cos Ysengrin took them away from him. 
Is Shadow 2 a shadowboy or shadowgirl?
Shadow 2 is a male.
Perspective [on ] in the panel when Shadow 2 is calling their attention about the door... he is in the wall and his foot is touching the door in the floor... right?
Is Shadow 2 getting his own voice now, seeing as his word bubble has changed colors? If so, what does it sound like?
It sounds like Annie and Kat at the same time.
Several sharp-eyed readers have pointed out that since Shadow 2 couldn't leave Gunnerkrigg on his own, he couldn't have entered it on his own. Will the question of how he got into the Court be explored in a later chapter?
No, but possibly a descendant.
Could you please tell us a bit about the shadow men? The fairies were able to understand Shadow 2 in the ravine, was he speaking a shadow man language or just baby speak? Do shadow men usually learn to speak English like Shadow 2 has?
He was speaking shadow man language, but not very well (not that we, as the reader, can tell). they don't normally learn to speak english. 
How did Shadow 2 know to look for Annie after she fell off the bridge?
He knew she fell off. 
When Mort was alive, was he a cutie?
I guess Mort was a cutie. He certainly acted the same.
Was Mort a student at the Court?
No he wasn't.
Then why is he haunting it?
Because that is where he is stationed.
When Mort makes doors disappear (as in Chapter Four), is he actually transforming them into blank walls, or just projecting the image of blank walls over the doors?
Will Mort's past ever be revealed?
Maybe, but not as a full on story.
Does Mort create illusions or can he actually alter reality?
It's all illusions, really.
Are Kat and Annie the only students Mort is friendly with?
Pretty much yeah. 
After their first meeting, has Mort ever made another attempt at scaring Annie?
Yeah he's tried as a joke. 
Is it Mort's 'job' to scare people? Or is it just something he does because there's nothing else to do?
It's his job. 
Seeing as it’s been in many questions recently, how do you think Annie, Kat, Rey and Mort would respond if they found out they were being paired up?
Kat would think it was funny, Annie wouldn't think much of it, and Mort would be comically embarassed. 
Does Mort remember his life, back when was alive.
If "Dulce et decorum" comes from "Dulce et decorum est pro patria mori" (Latin for "It is sweet and fitting to die for one's country") and that phrase is written in places whereMort hangs out, it could be a clue about how he died. Am I right?
what would mort's opinion of the ghostbusters franchise be if he were aware of it
He thinks it's a hoot.