They say the bathroom is the most dangerous room in the home.
I've never had a problem with developer staining anything except clothing. I've spilled it on the linoleum floor in my own closet--err, darkroom--and it mops right up. However, it's a good idea to pour carefully at the drain with plenty of running water.
Do be careful using electricity around water. But that's just common sense.
You do not have to have stop bath. You can rinse in a high volume of running water for 30 seconds. Developer is alkaline; the stop bath neutralizes its alkalinity, which both stops the development action, and prevents the alkaline developer from changing the PH of the acidic fixer.
Filling the film tank with water (or, for that matter, fixer) will dilute the developer remaining on the surface of the film, which will prevent it from having very much additional development effect. And a good rinse will remove enough of the residual developer to prevent shortening the life of the fixer. So, you can use water--lots of people do, and have for years. Some swear stop bath is just a way for The Man to separate you from money which you could spend on film or other goodies. Personally, I use stop bath, mainly for consistency. On the other hand, lots of people use Hypo Clear to speed up the wash; I never have, because I don't (personally) see the need.
Hope that helps!