In Which the Cockles of My Heart Are Reasonably Tepid

I've noticed that most MGs that have sold recently have NOT been 'school stories'. (At least what's listed at Pub. Lunch) Does that mean 'school stories' are history? Or maybe they are being bought but not reported? Any ideas?

I don't know what you mean by "school stories". A story in which the characters are in school? But that's... most of them. I'm confused.

Normally, if I get a rejection, I put it in my pile and go on, but I received one recently that makes me wonder. If an editor takes the time to point out exactly what does and doesn't work for her in a picture book, and says that it's close, but "not quite there yet", does that mean that she would be open to considering a revised version with those changes implemented? I know "no means no" is the general rule, but it seems like an awful lot of time on the editor's part if she doesn't want to see it again. And if she doesn't want to see it again, I don't want to come across as overly aggressive by sending a revision or emailing her to ask.

No means no. Invitations to resubmit are always explicit. You should take this as encouragement, though-- your manuscript clearly warmed the cockles of the editor's heart enough for her to want to take the time to give you feedback. Most of the time, speaking personally, my cockles are not that warm.

As a children's book illustrator with an agent, what should I be expecting from the relationship? I recently accepted representation with a great agency, but I'm not sure what I should be expecting as I don't currently have ambitions with submitting my own projects. Is she involved in my self promotion to help me get new work, or does she just help me with the issues that come up (contract, negotiation, etc) after I bring in projects on my own? As an editor, does it make a difference to you if an illustrator is agented or not?

This varies from agent to agent, and you should be asking your agent these questions. You should really have asked before you signed with her.
As an editor, no.

I was interested in your explanation of the fact that the author of a picture book manuscript should not expect to have any say in the illustration of their book. My question, then, is how an author/illustrator gets a book published. Is that situation always one where the person has an established presence as an illustrator? Do they submit the manuscript and not mention their hope to illustrate until after they have a publisher? Or maybe they're always established authors, and have a relationship with their publisher that allows them to present the idea? I can think of a lot of ways for such a deal to come about, but what's the typical scenario?

They submit illustrated manuscripts, and the editor doesn't look at them and think, "Well, we'll get that illustrated by someone better." She thinks, "This is essentially done! Awesome!"