Is the name Fitzpatrick Irish or Scottish?

Answer 1

That is a false dichotomy.

The name Patrick was originally Latin and means a "nobleman". It became popular in Ireland due to the work of the first bishop, Saint Patrick.

Fitz is Norman-French for "son of".

The surname Fitzpatrick would therefore have been given to the descendants of a nobleman named Patrick. He in turn would have been given this Irish name because his family had settled in Ireland, but in fact his father or grandfather would have been a Norman baron who had invaded Ireland and built himself a castle by right of conquest.

After a few centuries, the family might think of themselves as Irish, but really their ancestry would be French.