Only if you want to keep them!
Proper identification is important so you are not treating the wrong type of tree. You may want to find a good identification or reference book or hire a professional to review your site. Look for the 5-7 leaflets arranged in an opposite fashion on the stem of the compound leaf (usually 7-12 inches long). buds are usually blunt tipped with 1-3 pairs of exposed scales. This may be difficult to identify in the dormant season.
This depends on the time of year and the stage of the life cycle of the insect. Trunk injections appear to be the best method of applying a systemic insecticide. Soil injections or drenches may also be effective.
You will have to treat until you no longer want the tree or until the insect is eradicated which may be unlikely. Results of testing on products that produce the best resultsare not yet available.
The insect can lay its egges on the ash tree, treated or not. If your tree has been treated then it should have the insecticide in its system to kill the larvae.