is the word sidhe (pronounced she, for those who don't recognise the word) Irish?
It's Gaelic, yes. Also spelled "Sí", which is more obviously shee in English, as "s" is always sh and fada (the ´ on a vowel) makes a vowel sort of longer. A dot over certain constants has been replaced by adding an h, as in dh, gh, etc.
More pronouced "Shee", but likely varies with locality.
It was Yeats that named the "Fair Folk" or "People of the Mounds" (= Aos Sidhe) simply Sidhe., which is Gaelic for mound or mounds.
People is more often daoine, but aos or aes (various spellings) also means people. Sometimes in folk myth they are called Daoine Sí or Daoine Sidhe
Welsh is "People of the Woods"
Another name is the "Good Neighbours"*
(All these variations exist in Gaelic)
They are Tolkien's Elves, as the Scandinavian Elves are small, dwarf like.
The North of England calls them Elves (some versions Thomas the Rhymer)
Sí or Sidhe is spelled "Sith" in Scottish Gaelic.
There are various kinds of Sidhe. One kind is vampire like and almost certainly part of (Irish) Bram Stoker's inspiration as well as Vlad the Impaler, Baobhan Sith in Scotland, I forget the Irish name. Leanen Sí might be related.
There are other completely different kinds of Celtic "Fairy" folk, not "Sidhe".
[* Not maybe because they where especially "good", but you didn't want to annoy them.]
Later the Aes Sidhe became conflated with the Tuath De, who became the Tuatha De Danann. Leprechauns are REALLY late folk myth as their name is a corruption of the legendary Lugh, who variously is a God, Aes Sidhe, or Tuath De depending on era.
Real History?
The Tuatha De Danann were renamed so about the 11th or 12th Century, earlier they are called Tuath De. They seem to correspond to Bronze Age Celts, defeated by Iron Age Celts about 500BC. They seem to have defeated at about 1800BC, the Early Bronze Age (Copper Age) people (2000BC to 1800BC), the Beaker folk, who did build court graves, but not the "mounds" referred to as entrances to the Otherworld or homes of the Fair Folk, or Fairy Hosts. Those mounds maybe from 2500BC, or 2000BC at latest.
The most unusual feature of the oldest pre-christian elements of Celtic myth, is that perhaps uniquely there is no Creation Myth.
The Aes Sidhe are myth, but someone built the "Mounds" The Mounds are NOT the "Raths", those are the remains of Iron Age forts, but things like Dolmans (originally earth covered) and Newgrange, Knowth etc.
EDIT: Oh, this is my 8K post!