>>>>>>>>>>>>>>>
1) What's his first name?
<<<<<<<<<<<<<<<

AFAIK, it's never been revealed in the manga.

>>>>>>>>>>>>>>>
2) I read that in the manga, he said that Tatewaki was his long lost son....
Is this true? And if so, who raised his kids?
<<<<<<<<<<<<<<<

Absolutely true.  Presumably, he did, until 3 years prior to "current
events" in the manga, which is when he left for Hawaii.  However, it's
not made entirely clear.

>>>>>>>>>>>>>>>
3) Ed said that mommy Kunou died from poisoning after Kochi was
born....
This can't be true, can it? (Sorry to doubt you, Artie...)
<<<<<<<<<<<<<<<

If it is, it's nowhere in the manga...

>>>>>>>>>>>>>>>
4) Just when did his Hawaiimania begin?
<<<<<<<<<<<<<<<

Again, there's no real indication in the manga.  It could have happened
before he went to Hawaii, it may have happened while he was in
Hawaii.  I suspect the latter, but have no evidence for this.