Would gille be correct?
Yes. Gille and balach are pretty much interchangeable except that gille can also mean servant.
Why would it not be :Tha cat agus balach?
Because "tha" means "is." They do not have indirect articles like "the" and "a" in Scottish Gaelic
Because that wold be"a cat is and a dog
Balach sounds like balahhhhh
I always remember balach as boy because it sounds a bit like ❤❤❤❤❤❤❤