how hard is it for a new mailman to learn his routes?

Depends on the mailman--if he is a fast learner, he won't have any problems, if he needs a map, tell him to get one, or draw a map of his route, in his own hand writing.

that will depend on the person, some probably never get the route down pat, others work it out in a few days

Easy. All the envelopes and packages have an address on the front.

Its not difficult, just like learning anything else.