I use the same oil as in the engine Mobil 1 0w30.
The genny needs to be run on a regular basis. According to Onan, 2 hours under a load each month if not in use.
I would careful about pouring in additives since in the Greyhawk, the genny uses the same tank as the engine. Also if sitting for awhile, more than 2 weeks, use a fuel stabilizer for both the engine and genny.
2012 Greyhawk 31 FK
Flat towing a 2008 Miata.