"First of the ninth", yeah, occasionally, but adding the year in like that just seems stilted to me.

Yeah, Cap, you wouldn't hear this very often. The "first of the ninth" thing alone would tend to be in a business context, say, setting dates for meetings or actions from meetings, etc. But there are times that the year needs to be specified, and at those times I reckon it would be spoken as "oh two" or whatever.

I was especially curious as to whether 1st September would be preceded by a the and have an of before "September" for everyone. I'd never write either of those, but I'd say (=read) both.