You can always slice the hotdog up if your pan isn’t large enough - unlike sausage the casing on a hotdog is more for appearance than to keep all the bits inside (hotdogs are basically solid tubes of stuff) so if you slice it in half to reduce its length you probably won’t notice when eating it.

Anything will do, if they are non-stick, you’ll definitely want oil or water, to help distribute the heat.

You need to do yourself a favor and go get yourself a proper frying pan/skillet. It doesn’t need to be an expensive or nice one, but if you don’t have one that can fit a few hot dogs, your kitchen is way under equipped.

I pan fry hotdogs all the time. I put a little water in the pan to help the hotdogs heat all the way through and then let it burn off and fry them a bit to get them slightly crispy.