M10 uses :- 1 no stave, end, no. 72 Mk1
4 or 5 no stave, intermediate no. 2 Mk1 (depending on what leaner you are using)
17 pdr gun uses :- 1 no stave, end, no. 68 Mk1
3 no stave, intermediate, no. 1 Mk1
As to lengths, I have no idea though you can probably work out what you need for the M10. It seems likely the field piece uses longer staves. The intermediates have a male fitting on one end and a female on the other, the ends have a male on one end and nothing on the other, the wood being rounded on the plain end.
The fittings are as Adrian has in his M10.
The poles you have look US for the wooden and quite modern for the ally but no idea on actual application. Definitely not right for the M10 though!