Dear anybody who designs houses

do you know how a toilet works and the plumbing temperature of that shitter?

NO!

Hmm. Depends on your local codes. Some jurisdictions are strict about things like that but outside of that there shouldn't be any problem locating it closer to the toilet. As long as there is proper grounding and a GFI.

why don't you just invest in a portable battery?
those charge up for hours and you can be on the toilet or anywhere you want with them