POP3 email is slowly disappearing. No one is including the ability to filter email (aka rules) in mobile email clients because it's really only useful for POP3. IMAP does filtering, sorting and syncing folders at the server, as it should be.
Anyway, that said there is one mobile email client I'm aware of that supports POP3-style filtering. And that is Maildroid. It does rules and you can buy a spam filter subscription separately if you want. $13 for the Pro version + the optional spam filter, extra cost.
I doubt Maildroid can import your rules, but I could easily be wrong. You can email the developer to find out. With luck you won't have to enter them manually.
I think Maildroid will import your calendar but I don't think it can do your Outlook contacts. Again, I could be wrong. Outlook is a semi-standard but not really standard who cares about standards oddball piece of software. That's why it requires specialized solutions. Maybe the mentioned CompanionLink will do the job to your satisfaction.
https://forums.androidcentral.com/e?...token=hZoDsDhX
Android since v1.0. Linux user since 2001.