I think you're okay. Here's what I'd do:
Battery - keep it in a cool place and you should be fine. Some folks will tell you not to set it on a concrete floor. That's an old wive's tale. Concrete is fine.
Propane Tank. Don't store it inside your house in case you ever had a leaking valve. Keep it outside. I don't see the need to tape up the connectors. If something were to get in there, just blow it out. You could just slip a plastic bag and twist tie over them if you're concerned.
I'd park the RV tires on Brick Pavers, Plywood or Plastic in order to keep the tires from having continuous direct contact with the dirt. Keep the tires covered to protect from direct UV damage.
Now - You say you are going to park the trailer on a "vacant" lot that is close by. Do you actually own the lot? If not, do you know who owns the lot and do you have their permission to park there? If not, you may have more than a battery or propane tank missing one day when the owner of the property has your trailer towed for trespassing.
Also make sure that parking it on the lot does not violate zoning restrictions.
