Yes
Chugger pumps are not self priming, do not run it dry, you need the help of gravity
I'm not sure what your system looks like, but I would run starsan or PBW through your entire system
My assumption being that if you have a pump, you also have the needed ports/connections on your HLT, MT and Bk
Theres no issue in running starsan or pbw through your entire system, not sure why you're doing this from a bucket only