"Q1. Which I think you have answered, is that US Letter is folded into 3 to fit the #10 envelope. An obvious issue is that this is somewhat narrow and would float around in a window face envelope. Is there a standard method of folding the letter to stop this?
Q2. We use a thing called a With Compliments Slip which is 1/3rd or 1/4 A4 and is added where a quick note is attached to other enclosed material. Does such a beast exist in North America and if so what size is it?"
A1. Not that I know of, although it's certainly possible using machine folding. If it's done, the excess is likely put on the top third, and that section carries the addresses. I've not had occasion to use machine folding (nor have I used window envelopes except for the No. 9 or 9 1/2 size enclosed as SASEs in material I've received).
A2. I don't know that such a size is available here. I suspect anyone having a need for this size either has it printed and cut at a print or copy shop, or does it in house, depending on quantity.