energizing both elements of electric hot water heater
Although different heater manufacturers have and could still do different things, they rarely would configure the heaters to operate both elements at the same time because amperage draw doubles, wire gauge size increases, fuse size increases and little is gained in heat recovery.

Pic below illustrates operation of elements on standard dual-element heaters with non-simultaneous operation.


Pic courtesy of A.O. Smith Co.


  Is it allowed (*) to energize both heating elements at the same time?


NO, unless the heater was originally designed for that. You can never modify equipment (especially a boiler) without manufacturer's permission.