How to be removed from googleplusdirectory.net listing

These contacts are apparently separate from the ones added by Google+. If I use the find duplicates feature to merge them, will their phone numbers now be associated with their Google+ profiles in Google's databases? Will this information be visible to other people? In short, will this violate my friends' privacy?

No, it depends on their privacy settings.

I seem to remember some scare where Facebook might or might not have grabbed phone numbers and associated them with Facebook profiles by picking them out of friends' phonebooks on their smartphones.)

That wasn't a scare, neither were the numbers "picked up", it was opt-in.

It looks like under an older Google Profiles system (such as Buzz) it was possible to have a pretty URL like you've found above. Google axed it as a default however, in part because it effectively exposed users' username / email addresses.

The best article I could find on the topic was this blog post, which mentions:

if you had selected a vanity URL for your old Google Profile those have been grandfathered in to point to your current Google+ profile.

They may be coming at some stage, in terms of anything from Google itself is this line in the product forum in March:

The team has actually decided to take another look at vanity URLs based on user feedback and will be talking about whether or how to proceed - rest assured that they have not been ruled out. Stay tuned for updates.

In the mean time there are a bunch of URL shortening services operating you could use, or if you have your own domain you can point that to your profile.