When I make my strings, I twist them before I serve them. That way, the twists get settled under the servings, I also find it easier to serve a round, twisted string than a flat straight bundle of strands that twist as I serve; and unwind if I relax. I serve the same way as the twists as that seems to keep things in place easier. Going the other way tends to untwist the strands as I work. Being right handed I work from the left along to the right. The serving tool is going away from me as it rolls over the top of the string.
It confuses me when I think clockwise or anticlockwise, I tend to fix the left hand end of the string and twist the right hand end. I twist so the top edge of the string is moving away from me, just like the serving tool does when I use it.
It looks the opposite way to a screw thread.
20 to 30 twists seems about right. It produces a string that stays "round" and smooth. Too many twists can start to look lumpy and too few seems to look flat in places.
Stretching with 400# is something I never bothered about. What I found more important was keeping the tensions equal in the windings as I made the string.It is so easy to pull a bit too much near the end, and produce a slack strand from one of the earlier ones.
My string jig has rollers on the tops of the posts. Once the string is wound on, I roll the string so it moves like a chain on a bike, and that allows any slack strands a chance to even out with tighter ones.
Recently, I made a stretcher, to see what it was all about. I liked doing the twisting under some tension as that bedded in each strand nicely against the rest producing a round string with almost invisible twists as it was so smooth on the outside. It is easier to serve the string on a stretcher, too.
One thing I find with serving is, the tension needs to be set well, so the serving is tight round the bow string. BUT also each winding needs to be kept tightly up against the previous windings. If each winding is just in contact with the one before, they will separate very soon when in use. I tend to raise the right hand end of the jig so I am serving uphill and the weight of the serving tool is pulling downhill towards the previous windings.