Some emulators, like FCEUX and BizHawk, have a Hex Editor, and I would like to know if looking at it (to see if you set up 20 E3 8F or 4C E3 8F correctly) is not allowed, because this may be considered cheating :)

Under the game rules section of the rules it states "Anything not possible on an original and unmodified NES, brick controller, and SMB3 cartridge is prohibited for runs. This includes but is not limited to..." So no you cannot use any memory viewer or tool built into an emulator for runs.

Ok. I guess the rules weren't clear enough for me to know :(

You can use it for practice though