1: Whoever replaced your bearings screwed up. The problem you are having is due to the right side wheel hub bearing not being where Mr. Honda wants it. (unless you mis-mounted the caliper somehow and all bets are off)
You can fix it by making the brake side spacer #13 shorter by whatever distance the bearing is out from its normal depth and adding a spacer washer on the sprocket side to compensate but you MUST make sure the bearing retainer is actually screwed in tight against the bearing and that the bearing is fully seated against the weld bead. If this weld bead isn't making the seat shallower then all you need to do is seat the bearing properly and tighten down the retainer and all should be well.
2: There's some confusion about bearing covers and retainers. The cover at the sprocket is just a cover. The threaded plate at the disc side is the bearing retainer (#7 on the parts diagram)
This retainer is the only thing that locates the rear wheel axially, without it regardless of spacers etc the wheel would slide from side to side a bit.
Tightening the axle nut compresses a sandwich of the right spacer (#12), right hub bearing (#37), inner hub spacer (#17), left hub bearing (another #37), sprocket spacer (#15) and left outer spacer (#13). The outer sprocket bearing helps take the drive chain load and if I recall correctly floats on spacer #15 and is not part of the sandwich. The wheel is located by the retained bearing by the disc, the left hub bearing should locate itself against spacer #17.
You have the outer spacers correct. The brake caliper is fitting funny because the whole wheel is mislocated to the left of where it belongs.
The "weld bead" is scary. Where and why was a bead of weld required?
The right side bearing with that retainer is meant to be fully seated in the original bearing seat, with the retainer threaded in fully flush. The bearings do not need to be "pressed in", they should be a snug sliding fit on both sides. The right bearing should be seated just by threading in the retainer.
If the retainer ring threads have been damaged, you need a replacement retainer - not someone with a welder to make the bearing seat shallower.
The other possibility with the welding is a bead layed on the inner face of the retainer, this would not cause any problem with the spacing though. Your mechanic is right about that, the retainer isn't touched by the axle or any spacer. Find out what was welded and why. If the hub was welded to make the bearing seat shallower your mechanic has destroyed the hub and owes you a replacement in my opinion.