1. To trim the tree correctly you have to cut the branches relatively close to their base.
2. To do the wattle correctly you have to recut the base of the branch so the associated curved element segment is eliminated. This allows you to work with a fairly straight "bow-like" piece.
3. I thought it might require more than one tree to make this structure and I stock piled three trees worth of branches before starting. Ultimately, I think you can do it with just one.
Anyway, if you want to lighten the load to the dump and your looking for something useful to do with your pollarding you might try this (or something else!).