I think it varies a lot between Brittany, Cornwall, Scotland, Wales, Isle of Man and Ireland. Also somewhat with which period of time.
I don't think the Wikipedia article is very accurate for Ireland.
Here the Blackthorn & Hawthorn more important than Elder as "fairy tree". A local dual carriageway built in last ten years split around a fairy thorn.
Apple is important, but I don't see that it has same significance as Hazel, Rowan and Oak, the three important ones. I'm fairly sure "Ash" mostly meant Mountain Ash, the Rowan. We have a large Rowan and a large Hazel we planted when we moved in here in 1998. Though we weren’t thinking of Celtic lore. We have Willow, Plum, Elder and Cherry we planted too.
I'd never heard of the Tammar as Manx Celtic stuff is quite different to Ireland, Scottish is far closer, then Welsh.
As well as trees, for Irish Celtic (which is the oldest surviving) you need to know about the rivers, wells, the four fire festivals (roughly between the Solstices & Equinoxes which are not as important), animals. Shape changing is a big thing. Difference between bawns, court graves, dolmen, raths, stone circles of different kinds, and the bigger older structures like Newgrange and Dowth.