As far as "upstairs toilet runs occasionally when I flush my downstairs toilets", I would suggest that while you have that cover off, have someone flush the downstairs toilet and observe exactly what's happening. Is it just adding a little more water to the tank? Or is it letting a little water enter the bowl, which in turn is causing the water to refill tank slightly?
As far as those globs over the bolt heads, I would leave well enough alone unless you have a leak between the tank and the bowl.