HTTP status code 500 and CKErrorDomain 15

If that is difficult or not, I can’t say. As to the “outside the home”: that depends on your security requirements vs. paranoia. I don’t mind using port forwarding in my router so that WebDAV is accessible the same if I’m at home or away. The alternative would be a VPN (which can also be set up on the NAS). You’d then have to turn on the VPN on your device(s) when you’re away.

There’s no requirement for remote sync just because of that – you could set your iPad to accept Bonjour connections and both iPad and iPhone to use Bonjour sync. Or the other way around.
Remote sync is only indispensable if someone else modifies your data while you want to receive these modifications at the same time. Like an assistant or a SO at home/in your office working on a presentation that you are about to give in another location. Or the other way around.