multi-email gnus setup questions

[Benjamin Slade <slade@jnanam.net>]

A few issues I'm stuck on. Partially owing to using multiple accounts,
perhaps.

(1) Splitting mail with multiple accounts.
I have this in my .gnus.el:

;; mail splitting
(setq nnimap-split-inbox "INBOX")
 (setq nnimap-split-predicate "UNDELETED")
 (setq nnmail-split-fancy ;; 
       '(|                                ;;
         (: gnus-registry-split-fancy-with-parent) ;;
	 ("List-Id" ".*help-gnu-emacs.gnu.org" "INBOX.emacs.help")
	 (to "someone@domain.net" "INBOX.someone")
         "INBOX"                          ;; 
        ))
 (setq nnimap-split-rule 'nnmail-split-fancy)
 (setq nnmail-split-methods 'nnimap-split-fancy) ;; 
 (gnus-registry-initialize) ;;

But it doesn't seem to create new folders/groups for either rule.  What
am I doing wrong?  Is it an issue of having multiple accounts?

(2) Splitting mail with Gmail/other apps:
Assuming I can successfully split mail, if I split into something like
INBOX.emacs, will other connecting non-gnus mail clients see mail in
INBOX.emacs as being in the INBOX?

(3) Customizing the C-x gnus menu:
Right I see things like nnimap+gmail1account:INBOX. Is there a way to
customize this, to look like FirstAccount:INBOX ?