Different trees do it at different times, but mostly starting in February.
old trees
Ireland has lots of trees, because it has the kind of environment that can support them. At one time very large areas of Ireland were covered in trees. There is still a lot of forest in Ireland.
Yes, red bud trees generally thrive in full sun, but they can also tolerate some shade.
after flowers have fallen off.
American Red-Bud trees are reported fine to plan in horse enclosures. Talk to your vet if you have any concern about a horse eating the buds.
Palm trees can grow all over Ireland, even though it does not have a tropical climate.
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Yes.
Many kinds of trees grow in Ireland. To give just a few of these, you could say Oak, Horse Chestnut, Sycamore, Cherry; many kinds of fruit trees like ones with apples, pears, plums; various kinds of pine trees and palm trees.
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.
possibly, if it wants to.
'Smoking trees' is slang for smoking marijuana (also known as Cannabis, weed, pot, reefer, bud, etc)