i used to be obsessed with keeping my heart rate up, breathing hard, etc. while lifting.
once i kept cardio (cycling) and lifting (heavier, more rest) separate, i started enjoying both a lot more. in short, there's enough to focus on while lifting, without having to worry about getting "cardio" in as well. i don't recommend it.
The headache thing happened to me twice on leg day in my life. It scared me the first time it happened, as I was almost blinded. Crazy shit.
As far as squats for cardio, I'd think it would make sense. I always got more winded from squats than any other muscle. Intense back workouts were a distant second.
i got these exertion headaches a couple times. i stopped eating a dozen eggs a day, and they went away. not sure if related

scary as hell... i went from being the most workout obsessed person on the planet to thinking "i'm going to have to take up running, i guess" in the span of about ten seconds.