Of course, a negative voltage equal to the forward voltage is dropped at the Schottky diode if it is at the input, for example, and a negative input voltage is present there. However, this is not a problem both at the input and at the output, as this forward voltage is typically well below the threshold voltage of the silicon pn junctions.
The maximum tolerable voltage depends on the current limitation before the Schottky diode, since the current must be limited either by the output resistance of the voltage source or by a discrete resistor.
As for short pulses, like the 50ns you mentioned at the output terminals, it depends on the effective voltage level of the pulses. If it is below the threshold voltage of the silicon pn junctions due to external Schottky diodes, there is no problem. If it is above, the behaviour is not defined, so this condition must be avoided.
Regards
/Peter