first with the switch open.... and as you said they float.... you need to make sure they don't float for one, and by the way M1 is connected backwards.
the gates are capacitive, and so opening the switch leaves them with nowhere for the charge to go. as a matter of fact this is one method i have for testing MOSFETS out of circuit with a DVM. i measure between source an drain and should get an open circuit. then i disconnect the + lead from the drain, touch the gate lead with the meter lead, and then source to drain will conduct.... this doesn't work with all MOSFETS as some have thresholds higher than the open circuit voltage of my meter, but it usually works.
to answer your last two questions, yes, the FETS will stay off since the gates can't bleed off their charge.... background electromagnetic fields likely won't turn them on because there's no path for induced currents, but electrostatic fields might turn them on.