I can see the appeal of "amn't I" instead of "aren't I", but would you really say "I amn't" instead of "I'm not"?
(Also this is the first time I've noticed that Standard English uses two completely different contractions depending on inversion... what a language.)
The English phrase "I'm free" can sometimes be interpreted as "I'm available", rather than "I have been released from jail", but no, as a general rule, available and free aren't the same.
For all of these, it's correct to say "nil mé" as well isn't it? And for example "ceannaim" can also be said as Ceann mé? Different dialects isn't it?