Yes, it's a really tight fit. The bearings are also pressed into the BB. You can do this at home with an assortment of washers and spacers and couple of high grade bolts (instead of the crank fixing bolts). First press the bearing on the non-drive side of the spindle using washers to assure that you press against the inner race. When you get the bearing to the appropriate location, leave the bolt and spacers in place. Go the drive side and fit washers and spacers over the spindle so that tightening the bolt on that side pulls the non-drive side bearing into the BB shell. Then press the drive side bearing into the shell with the washers and spacers from the other side. PM me if you need a batter explanation.

The bearings are 6003. They are commonly available.

Take the fork problem seriously.