When I go to the gym, I usually wear a bandanna instead of a ponytail. Will wearing a bandanna while you are sweating make your hair fall out??? Will it give you some sort of scalp disease also?
No, bandannas are just cotton in contact with your hair and skin. Remember your hair is in contact with cotton all night, the cotton of your sheets and pillowcases, and it survives this just fine. As for bandannas when you're sweating, they are no different than any other cotton clothing that gets sweaty, like your jeans and t-shirts. After years of sweating in these things, comfort yourself with the thought that your leg and chest hair has not fallen out. :-)
Cotton doesn't hold moisture in like rubber or leather does, but rather, it absorbs moisture and draws it away. So your bandanna isn't going to cause anything to rot up there, and if anything, it should help keep things a little drier.
Of course, like with all cotton clothing, you gotta wash 'em, dude. If you don't for days, the oil and sweat buildup will eventually irritate your forehead and the skin there will break out. Bandannas are made of a much thinner cloth than are jeans or shirts, so washing one is quick and easy. It will easily line-dry overnight, so if yours needs a wash, just do it in the sink and hang it up to dry. It will be ready to wear in the morning.