Right I've read both of these from cover to cover dozens of times (bought both as soon as they were avalible) so i can answer your questions I Love Vergil. The rabbit was origonaly Alices doll but was possed by a deamon. He serves no part but to link the book further to the Alice in Wonderland idea.
The guy with the hat, I'm pretty sure is Arkham. In the first book he tells the rabbit he'll talk to vergil then Virgil ends up with Arkham. In the second book in one scene virgil is by a window and the light from the full moon shows his shadow as a deamon, while a few pages later (or maybe earlier) Arkhams shadow is of the hatter. Right near the end theres one scene when the hatter has the same style eyes as Arkham and virgil seems to reconise him and talk to him about what him and Arkham are upto. Also the Mad Hatter is a similiar idea to Jester.
Well i think i just explained how they know vergil on the one above
And the same with Alice again
Though I have noticed a few inconsistencies with the manga. Firstly in the first game in the description of Nobodies it says that they were never given a name, but in Code 2 it says that a deamon is it's name (thus doesn' need to be given one) and a nameless deamon is powerless while the nobodies are far from powerless.
Vergil is supposed to use Iadio as his fighting style with Yamato, yet in Iadio the sword is held in it's saya (scabbard) blade up, yet in the manag it's blade down (in the game he has it the right way up).
There was something else I noticed that was out of place but I've forgotten for now, so I'll post that when i remember.