Some of the plants on that list are really easy, others were added on advice from others but I have had zero success so far. Elms and Hawthorn are 2 of the types we use that are easier so worth trying for beginners. It is highly likely there are other species that can grow from root cuttings but no-one has thought to try or added the to the list. If it is not there it is always worth a try just to see for yourself.
Timing is more about the tree's natural growing cycle than calendar months after taking the cuttings. Start looking for buds and shoots a few weeks after the species normally leafs out in your area.
You should see buds around the top of easy species in a few weeks and shoots growing in a month or so after the species normally leafs out.
Some of the more reluctant ones do take 3 or 4 months to sprout new shoots.
I can usually pick failed cuttings when they start to shrivel up. Occasionally some will die back a bit at the top but are still OK further down and will sometimes shoot. I have had trident maple root cuttings stay healthy and solid for 2 years but none have ever sprouted so while looking good holds hope it does not always mean success.