I'd empty both tanks and flush the black tank... Then add five gallons of water and a chemical pack to the black.
As far as leaving it connected to power that shouldn't be an issue. Our last motor home was plugged in to shore power all the time in storage. I'd be a bit nervous about leaving an external power protection device hanging out for a week.
I always turn off the water if we are going to be gone any length of time. I had the small clean water hose come off a toilet and flood the rear of a trailer. I came back to a nice waterfall coming out under the door and down the steps...