No extra grease needed but I would wipe the race with clean new grease.
Yes tighten the spindle nut fairly tight while slowly rotating the hub to set the bearing. Then back off and finger tight then loosen to the next cotter pin hole. There should be very slight play in the bearing to allow for heat expansion.
The whole bearing buddy and ez-lube filling the cavity and keeping the grease under pressure is designed for boat trailers that submerges the axle during launch. The system generally prevents water intrusion to the bearings. Just an extraneous feature that can remain unused for RV trailer use. I recommend not filling the cavity.