J1 Visa

I am a Canadian citizen by birth, and I have been with my fiancee for
3 years, we currently live together in Canada- he has dual citizenship
US and Canadian. (He was born in the US)

I was planning on applying for a J1 visa, and doing an
internship/traineeship while living with him in the US- this way we
can live together, I can be there legally and we can plan the wedding.

I've been told that because I'm Canadian the 2 year HHR does not
apply- (I'd be training in the Art/Entertainment industry- nothing
government related)
Since I'm Canadian, I believe I'm granted J1 "Status".
.
Can I get married while in the US on a J1 Visa because I've entered
the country legally?
Or would this be considered immigration fraud (even though I will be
training in the US)
Can I adjust my status while on a J1 after we are married?

You cannot come with the express purpose to marry, to my knowledge.