Can someone explain to me how I can trade between my own planets? And transfer resources?
Just build a Merchantmen/Bulkfreighter fleet at your home planet and send it to one of your colonies. Transferring resources is done through planetary links that some people have when planets are spaced out a lot, for those you just build as if you had the resources available.
From what I understand, merchantmen do this pretty much automatic; do I need to keep setting their route?
Nope, they'll just pick a profitable planet and move to it next, returning to their home planet after a few stops.
Can I create a fixed route that they keep going on?
Yep, I think if you create a circular route and have it stop at planets they'll follow it, return home, then get back on it again (not sure about non-circular routes).