- Making your own or acquiring cutting tools that fit in such spaces, e.g. able to thread up to a shoulder at that scale.

- Measuring your progress. I'm really not sure how you'd measure pitch diameter for such a small screw without exotic measuring tools. Perhaps you would just cut it to fit the mating part, which on it's own would still be difficult to check due to the subtlety of the feel of such a small screw going in.

- Cutting internal threads. I imagine making your own M0.6 tap would be quite tricky as you'd have to grind very small reliefs after making an M0.6 screw.

Definitely not using coolant on parts this small; small amounts of lubricant if anything. Supporting the part shouldn't be much of a challenge as you would be taking requisitely small cuts with very small forces. I'm sure tweezers and loupes/microscopes are your friend when making watch parts.