What happens if you connect the neutral of your home to another transformer's neutral?

Answer 1

If you independently connect two different neutrals together, you violate the star concept that protects the grounded neutral. While neutrals are all grounded, their relative potential voltage could be sufficiently different that connecting them together could cause large eddy currents that might cause overheating and equipment damage. Neutrals in one system are only allowed to be tied together at the distribution panel serving that system, and inter-system cross-ties are not allowed. Violation of this rule causes violation of the principle that is embodied in Kirchoff's Current Law, i.e. that with only one path to ground, any current on ground must represent a fault - cross tying systems together prevents detection of that fault, along with introducing eddy currents.