ALl drinking alcolhol is ethanol - CH3CH2OH. Phenol is another type, as is methanol (found in antifreeze), propanol (isoporpyl alcohol is rubbing alcohol) and many many others. Basically an alcohol is a molecule with an -OH group on it.
There are nasty side effects of drinking non-ethanol alcohols. You’ve probably heard of kids having serious liver damage, or blindness, or death from consuming antifreeze. Ethanol is the only “safe” alcohol to consume to get a buz.
As for who you get a hang over, it is strongly related to dehydration, as well as how well your body can metabolise the alcohol you consume. There is a limit on how rapidly you can degrade ethanol, and consuming too much can cause illness because you can’t get rid of it fast enough.
I’m not sure why different alcoholic drinks mix badly, although I do suspect that it has to do with the other components in the drink. Beer has a lot of carbohydrates in it, which requires your body to break it down differently than wine, for example. Mixing the two likely requires your body to pump out many more degratory proteins than usual, thereby putting stresses on your liver and body biochemistry, which make you feel ill. This is a bit of a WAG, though, so take it with a grain of salt. Although if you’re going to be drinking a lot, take in a lot of water too, since metabolism of ethanol dehydrates you, and that WILL give you a head ache.