You are responsible for keeping the contact information up to date (which you also have to do if you're using a privacy service). Beyond that there's really nothing you have to do.
For your specific questions:
Am I expected to read all the emails sent to my email contact? (Or just some?)
We would really appreciate it if you did. Especially if you're the tech contact and someone emails you to tell you that something is horribly grossly misconfigured about your domain. Also if someone wants to sue you for having a name they think they're entitled to I believe those emails/postal mailings go to the admin contact.
(In practice it's just going to increase your SPAM volume. You can ignore it the same way you ignore your regular email.)
Am I expected to answer the phone and engage callers in conversation?
I've had domains listed with actual contact info in Whois for longer than I can remember and I've NEVER gotten an actual honest-to-god telephone call from anyone related to them. If someone calls you and they're not offering you an extortionate amount of money to give them the domain I suggest Ben's solution of screaming and shouting expletives until they go away. :-)
Am I expected to answer the door should someone turn up at my postal address?
With two shotguns in your hand, while screaming and shouting expletives, because they'd be some pretty creepy people. Again I've NEVER had someone actually show up at my door, but if you're worried about that I believe a PO Box is acceptable for a mailing address.
You may get some postal spam though -- Read and ignore as you would with any other postal spam :-)