There is no way that a hot wire could have been twisted together with neutrals. There would be a direct short and a blown breaker.
There are cases where a white wire can be hot, but it really should have some black tape on it to identify it as hot. An example is a switch leg, to a light fixture, where the hot wire is in the box supporting the light fixture. A standard 3-strand wire (white, black, ground) is used to send the hot wire down to the the switch. When I do it, I connect the white wire to the hot (black) in the fixture box, sending the hot side down to the switch with a white wire (which should have black tape near the end). The wire coming back up from the switch is black, so the fixture is connected to a black hot wire and a white neutral.
Two circuits in the same box is a no-no, unless it's a case of using a shared neutral. In that case, the breakers are linked together or a 2-pole is used, so both must be shut off at the same time. You can supply two circuits with a 12-3 or 14-3 wire, using only one neutral, as long as both the black and red wires are hooked to different phases. If that's not done, then the neutral would carry the amperage from both circuits and fry.