Yes. There are a lot of oak trees and many other kinds of trees in Ireland. Derry, an Irish county, is called the "Oak Leaf" county and has an oak leaf as an emblem, because of the amount of oak trees that it once had.
Yes, ash trees are commonly found with oak trees in some forests. In northern Texas for example, it is common to find Green Ash, Texas Ash and White Ash growing near Red oak, Shumard Oak, Post Oak and Burr Oak.