No, I'm not a native speaker. I wouldn't even consider myself fluent. I stuided three years at college and also spent two summers doing immersion programs, in Galway. I just fell in love with the area, so that's who I pull for in things. And you are right, the biggest Gaeltacht is in Galway. I'd love to live there.
❤❤❤❤❤❤, I'd let cut myself for one of those immersion programs for Irish learners. Here in Poland barely anybody heard about such language and there's only one textbook available, without even a CD or any kind of listening tracks, which, considering quite ethymological ortography of Irish, is quite a disadvantage. That's why duolingo is so great doing that course ;) I'm also planning a trip to Ireland in a year or so so I could try the language myself ;)
The Polish textbook (An Ghaeilge by E. Gussmann and A. Doyle) seems to be considered a very good one on Daltaí forums. And as far as I can tell, it is good (however, it does not teach you Caighdeán Oifigiúil but Munster dialect). ;-)
Ten polski podręcznik zdaje się być uważany za naprawdę dobry na forach Daltaí. I, o ile potrafię ocenić, faktycznie jest dobry (choć nie uczy irlandzkiego standardu, tylko dialektu munsterskiego). ;-)
"clock" may come from Celtic, but not from Irish. It started with Latin cloccus, which gave French cloque, then Dutch klokke and English 'clock'. The Proto-Celtic word that Latin may have taken is reconstructed as klokkos, but Irish clog comes from the Latin, rather than that word. https://en.wiktionary.org/wiki/clock#English
That said, carr may very well be a native word - the Romans took a lot of words about horses and transport from the ancient Celts.
As far I'm aware it really hasn't gone both ways. Aside from a handful of words - "galore" and "trousers" spring to mind - Irish seems to have had very little influence on English vocabulary.
However, I have read that the use of auxilliary verbs to form questions in English - saying "Do you eat cheese?" rather than "Eat you cheese?" - comes from a time when native speakers of Celtic/Gaelic languages were first learning English and subconsciously or otherwise altering its grammar to fit the patterns they were familiar with.