I have no problem believing Anakin found the parts from a broken down protocol droid lying around Watto’s digs and put it back together. I don’t think we were ever meant to think he machined the parts himself or anything like that. As for blowing up the ship, that was dumb, but the movie’s been hitting us over the head with how inept the forces of the Trade Federation are for two hours by that point, so it isn’t a huge leap. C-3PO’s barrage of one-liners spoken to no one, the sudden appearance of R2-D2’s rockets, and the notion that every single droid head is totally interchangeable coming in the span of five minutes are all much harder for me to swallow.