(3) hageshii is the adjective. The -sa form turns it into a verb as Mike said.
It could mean violence, or other things like intensity, ferocity, severity.
I don't know the song but I doubt violence would be the best translation.
(5) Yes, basically. Note this is correct grammar. Instead of prepositional phrases, you can put an entire phrase ahead of a noun to modify it.
I, who can't hide my temper.
(6) boku no is "my." So it becomes my hou. Or my way, side, or part.
Something like:
It's my fault, I who can't hide my temper.