Aren't these just loan words taken directly from Latin? I.e. that's an example of influence, not common roots. I suggest that "an fear" and the Latin "vir", as in virility, are a better example of that shared heritage. (I am just starting with Irish, but I'm a linguist and have studied some history of languages.)
Just the reverse Igor. Many Latin words (and Greek) were taken from the Celtic Language. You have to remember that the Celts covered most of Europe and parts of Asia Minor and invaded Italy/Rome on various occasions. Of course, christian clerical words would have been taken from the Latin with the later introduction of Christianity. Take a look at the introduction to John O'Brien's Irish-English Dictionary 1836 (do a Google search).
This sounds nonsensical to me as far as Greek is concerned, at least for the most part. Greek has had very little direct interaction with Celtic, if none at all, the way these things go. When Celts invaded Greece, Greek had been there for millenia. Plus the idea that the odd invasion of nations that Greeks perceived as barbaric could really influence their "done" language borders on historical absurdity. In this case, the word "cathedral" comes straight from Greek, "cathedral" - καθεδρα - κατα (καθ) + εζομαι = down + lie/be and the έζομαι word comes from IE (sed). So both you and Lancet are mistaken on this. Either cathaoir is a loan-word or there is no relation. "Καθ" comes from Κατά = down (Preposition). Maybe that comes from a common ancestor word. I don't know if that's the case but that would mean that both languages developed their own similar sounding words for "sitting down". It's really tricky to study etymology if you don't have any knowledge of Greek. It's like shooting blindfolded. So your best bet would be that Celtic borrows heavily from Latin which borrows heavily from Greek.
There are two L sounds in Irish — a “broad” L, and a “slender” L. A broad L is like an English “clear” L, as in “lee” (but note that some English dialects only use the “dark” L, as in “full“); a slender L is described above, in my reply to artiguesmommy.
Note that some dialects of Irish can have up to four L sounds (two broad varieties and two slender varieties), but that’s primarily of interest to phonologists.