There is no way anyone here can give you any kind of educated (and safe) answer
to your question about tires and rims ..... Take what you have to a tire shop
for your own safety and piece of mind that your wheels and tires are mounted
and balanced correctly.
If your rims are rusty or dented, they may not hold air for very long.
A trailer wheel blowing off at 60 miles per hour is not a very safe scenario.
as for the Bearing Buddies, in MY world, because I just did one of my trailers
last month (I have 5), I would put in new seals and new bearings first, then,
install your BBs. Purchase a grease gun with at least a 18" flexible hose. Fill with MARINE GREASE.
(the salesman at the auto parts store will show you how to load the grease gun).
pack your bearings, put in the back bearing, fill the hub cavity as best you can with grease.
put in the outer bearing. Install the bearing buddy and pump your gun s-l-o-w-l-y until
grease comes out of the little vent hole. news paper under your project will keep grease off
the ground.
If the BBs are really snug, use a wood block and gently tap with a hammer to get them seated.
any questions - - - go to YouTube - - - many good videos on how to do it.