I just discovered freeshell.org tonight. What a great service! I have been looking for something like this since the start of the year because I will be losing my uni webspace when I graduate at the end of the year. My site is currently PHP based and I wasn't liking the prospect of finding a cheap replacment that would host it. Well it looks like I have found my solution. I might even go the whole hog and get a ARPA membership. Once off $36 sounds like a very good price to me. As for IMAP DAV I didn't see any reference to it so I guess that's a no, of course if you are a suitable member ARPA(?) you may be able to put in a request for the mod_dav apache module.
Edit: Just found this in the freeshell faq (type faq in a shell)
[03] WHAT IS THE POP3/IMAP AND SMTP SERVER ADDRESS HERE?
For both of these services, please use 'pop.freeshell.org'
or 'mail.sdf-eu.org' depending on which site you use.
Your POP ID and password are the same as your login account.
SMTP is now done by password authentication. Due to the
method we've chosen, only VHOST and VPM members may use the
SMTP server. The SMTP server is 'smtp.freeshell.org'
If you're really desperate to use our SMTP server and don't
need to VHOST, we HIGHLY recommend a VPM account. Check
out the answer to:
CAN I GET EMAIL USING '@USERNAME.FREESHELL.ORG'?
For more information.