For the pinion, the hole is probably a nominal 12.7mm - or half-inch as us old-timers know it! Easy enough (but not necessarily very cheap) to get a reamer for that. Biggest issue is maintaining concentricy. Personally, I would hold it by the teeth in a collet. You can make a one-off collet which will be very accurate even if you only have a tired 3-jaw chuck. A drill to open out the hole might work but a small boring tool would be better, whether or not you use a reamer for final sizing.

From what I can see, the shaft is more difficult. Even if it's not hardened, I'm not sure how you will hold it for turning which you will need to do before cutting the thread Possibly another home-made collet would do. Assuming it's just for a securing nut rather than an accurate location surface, a die would do the threading job but there will be a groove between existing thread and shoulder that might give a problem. If it is hardened - make another one from scratch?