Literally A cat is with me
It's a very similar construction in Irish.
Tá cat agam = A cat is at me (literally).
Same in Scottish Gaelic,
"Thà cat agam"
A cat is literally with me as I do this lesson!
So, "fi" is the mutation of "i" then?
No, Fi is the base word and it sometimes is said as "i" because it is easier to say.
Actually, "mi" is the base word and "fi" is the mutated form.
Yes, in more formal registers though typically courses teach "fi" as the starting point in order to simplify things.
Mi gen i gath.
It's "Mae gen i gath". Literally "a cat is with me", in that sentence "mae" means "is".
Mae cath gen i
Mae gyda fi gath
Are those all used?
I was under the impression that it's Mae gen i gath and Mae cath gyda fi but not the other two orders.
Yep. Gen is northern (and it changes form depending on person) and gyda is southern (gyda doesn't change). The order just changes the emphasis.
Are you suggesting that it should be an acceptable answer?
It is what I have learned at my class in North Wales
I'd recommend you check with your tutor about that, the only third person singular form of to be is "Mae" with dialect pronunciations of "Ma"