I mean, it's more a manner of speaking.
Literally, it's "I am at home in the Town of the Ford of the Hurdles."
Saying you are "Living" in a place doesn't translate well at all, it would sound like saying "I am in existence in this town."
As for Dublin, that's a funny one. Dublin itself is just anglicised Irish, "Dubh Linn", meaning Black Pool in reference to the pool that once existed under Dublin Castle. However, native speakers came to call it Baile Átha Cliath, as to most people, it being the last place you're able to FORD the Liffey was more important to them than some pool that used to exist. As for hurdles, those are the mats that lined the banks to give traction with the amount of mud in place. Basically, the Irish speakers tended to be lower class, so the ford of the hurdles was the biggest feature of the city, then a town. As such, in spoken, informal Irish, it became "Baile Átha Cliath".
Dublin, despite being more Irish sounding than the literal translation of "Hurdlesford", ended up what the English called it, and the Irish formed their own name.
I'd love to hear this in the slow version, since I can't make out at all how "mBaile Átha Cliath" becomes what sounds to these ears that aren't at all familiar with Irish like "im law Clee-ha." I'm guessing that what sounds like im-law is "i mBaile" and that Cliath is Clee-ha. I don't know what "atha" is supposed to sound like on its own (is it at all like ata?) and I don't hear a thing here and maybe that's just the way it is, but I think I'm just going to have to memorize this one!
This is an Irish-to-English exercise, which means that if you were entering an answer in Irish, then you were asked to "Type what you hear". If you heard Táim i mo chónaí, you were marked "wrong" because she didn't say Táim i mo chónaí, she said Tá mé i mo chónaí.
If you had been asked to Translate from English, then either táim or tá mé would generally be acceptable, but that isn't what this exercise was looking for.
The Irish course relies on actual recordings. Many other courses use computerised text-to-speech engines to read the text. Duolingo doesn't provide slow versions of the recordings.
There are instructions for accessing the audio directly in the stickied post Irish Pronunciation Guide. When you have direct access to the audio, you can slow it down, either in your web browser, or in a 3rd party audio player.