the nail rusting does not produce much useable soluble iron, more mess than it is worth. You want chelated iron. You can get a pound of chelated iron (in EDTA or DPTA) for $10 that will last a lifetime.
I would avoid the EDTA as it can cause PH instabilities.
not true at least in the amounts you would add to fert a planted tank.
Just something I have read multiple times on forums but we all know how the internet can be a haven for misinformation...