This warrants a much more detailed answer than I have time for now.
Tripwire - install in templates, store db in offline vault - I'm looking
for changes in /rw, as well as "normal" directory structures.
Mutt - varies according to provider. I set this up when I was first
playing with Qubes.
I use 3 qubes: one disposableVM to pick up mail - either offline imap or
rsync mail dirs. That qube is minimal, connects over Tor, and is restricted
to mail provider.
If the sync is in Mbox format, you can use mb2md to convert to Maildir
format.
The mail dirs are synced in to my mutt qube which is offline. I use
qrexec for this.
Mutt is a great MUA, and has good integration with PGP. I use split-gpg,
of course. I use notmuch integrated with mutt to keep on top of email.
For sending mails I use msmtp. Actually I queue outgoing in the Mutt
qube, and rsync the queues (over qrexec) in to a sender disposableVM,
which has outgoing traffic restricted to SMTP host. Over Tor of course.
So the fetch and send are done using disposableVMs, and the message
queues synced in and out of the offline mutt queue over qrexec. The
disposableVMs use minimal templates, have restricted network access,
and use different network routes.
The mutt qube is also based on a minimal template, and has a mailcap
that effectively loads almost all attachments in offline disposableVMs.
I have keyboard shortcuts to trigger the receive and send sides - I
suppose you could do this with cron jobs, but I prefer not to use
automatic processes.
That probably raises a few more questions. If it does, ask and I'll try to
provide some specifics.