There is already a patented disposable corn plastic strainer, but it is the divoted kind, rather than a flat mesh sheet that lays across the sink. (since 2010)
There is already an enzyme drain cleaner (since 1966), but I would want to have people use this on a regular basis, like shower spray, after each use or daily. I'm not sure if that makes it different enough.
There is totally a drain shaver already! That is so cool!
There is thankfully not a patent on a drain monster. There is a vermiculture compost bin, however.
There are flat screens as drain protectors, but it would be easy to alter one (a la the coffee cozies), to become patentable.
I didn't find a patented mesh drain ball.
I didn't find personified drain covers.
I didn't find a drain mill.