I won't give any quest information, but it seems to me that neutrals should be able to do the good quests after the guild ones as well as the evil. I mean, some of the ones you have to do for the evil are, well, pretty dang evil.
Umm...Evils
No they cant, if you know what one of the goodie quests entails, a neutral could not do it.
Hrmm...I guess I don't play goods enough. Can't remember what it is, but oh well. It just seems like with the whole children thing, neutrals wouldn't necessarily be inclined to do that.
You dont HAVE to do the quests, it is optional.
And I can only think of ONE goodie quest that a neutral couldnt do. Well they COULD, and I suppose it would work, but they wouldnt be following the spirit fo the quest 
neutrals could do all the quests that goods can, but not at the same level the goods can do them. I think a smart change would be to split them up maybe. Let the neutrals do some for xavier and some for himmah, or give them a whole new set. Or leave them the way they are, I like them just fine as long as I can do them.
Once upon a time, wasn't the set of quests a neutral got dependant on their race/class? Or something like that? I seem to recall running into the problem Mister E is talking about a few times.
Anyway, my personal preference would be to give neutrals their own set of quests, but I think it works fine as it is.
I think it was based more on your ethos if you were a neutral. I seem to recall if I was a lawful neutral I was going to Himmah and if I was chaotic (98% of the time) I was going to Xavier. Been a while since I've tried anything like that, but I believe it still goes like that. Then again this was for Gnomes every time, never tried any other race.
That would make sense, seeing as how I rarely (never?) play anything not chaotic.
Heh, up until pretty recent...a neutral could go do Himmah's quests(one you DID have to do differently) then you could go do Xavier's, making Neutrals own the Master Questor all the time.
I think a character should be able to choose, but once he accepts a quest from Xavier, himmah would no longer accept him, as if he accepted one from himmah, xavier wouldn't.