She's so cute. My grandfather had many beagles for hunting. They were good around us kids too but they liked him best. They can be vocal and like to "run" and be outside but if she was raised indoors I guess she likes it. Good luck. I hope she won't be lonely since she's used to another dog around.
Yes, if she's used to being inside and they normally like to hunt she would take off unless she's trained very well. The peeing inside might be her nervousness at being in a new place. But I hope you did ask if she was house trained. If she isn't (or wasn't trained properly) at her age it could be a problem.
But good luck. And good for you for adopting her. I've had bassets and a bloodhound as an adult and they've been wonderful.