So I'm using an Ubuntu phone. While compared to other phones you're certainly
more free here, it's not fully free in any way, so I don't know if it is
relevant for this forum/list, but I can give you some answers to your
questions:
>I'd lke to be able to sync contacts and calendar with a POP/IMAP email
program.
I use syncevolution for this. I don't think there's a GUI for this (at least
there wasn't when I started using Ubuntu Touch), but you have access to a
terminal anyway so it's easy to configure and sync from there. I have my
calendar/contacts stored on a server that supports CalDAV and CardDAV, and
then just sync it everyday. That way when I make a change somewhere else, it
will propagate to any of my other devices after the sync. Of course you could
also write a cronjob for this, most of GNU tools and standard tools that you
know from a Linux environment are available on the phone. (As long as they
work with ARM.) The only thing that doesn't work for me is GnuPG, and that's
why I don't use E-Mail at all on my phone, because all of my mail is
encrypted. There is an e-mail client that is kind of decent (Dekko), but
that's it.