Welcome to the forums!
For the missing tail lights, you will likely have to buy some used ones from a salvage trailer. Have a good look at the Forums Classifieds, and maybe you will get lucky. The ceiling assemblies may still be available from Inland or Outofdoorsmart.com Things like this are also sometimes found on Ebay. You might also post a "wanted" add looking for them.
For the running lights, you are going to have to do some detective work--you will need a volt-ohm meter. Start with your tow vehicle and make sure you have running light power at the plug, next, plug in your tow lead and check to see that you have power at the trailer. There should be a little cover on the inside of the trailer that gives you access to the back of the plug at the wall. If you find that you have 12 volts to the clearance lights all the way here, but no lights, then things get stickier. Put a volt-ohm meter to the wire that leaves the back of the plug going to the clearance lights (it is probably green), and check resistance to ground--it should show a few ohms. If it is wide open, then the wire to your clearance lights is disconnected behind the wall somewhere before the first set of clearance lights (which is in the front).