For most (if not all) audio power amplifiers the output impedance is a fraction of an ohm and the speaker might be 4 ohms. The point I'm trying to make is that you don't match a speaker impedance to the audio amplifiers output impedance because the audio amplifier's output impedance is (usually if not always) much, much smaller than the impedance of the load.
Firstly, when we are in bridged mono, it would theoretically give
400W. But what happens to the output impedance: Does it remain the
same, halve or double - 16, 4 or 8 ohms?
So, say the output impedance is 0.1 ohms (as per my earlier words), in bridged mode this would approximately double to 0.2 ohms but, as I previously said this is unrelated to the speaker impedance. The reason why amplifier manufacturers quote a speaker load range is to prevent overload and out-of-bounds distortion. Matching is not involved.
Secondly, is it safe to use my 8 ohm speakers if I keep the power low?
Yes it is. Reason: think about an 8 ohm speaker with a centre tap winding exactly halfway along the speaker coil. Now imagine what AC voltage you would see there when used in a balanced bridge. If you can't imagine it I'll tell you - it is 0 V AC and therefore two 4 ohm speakers with one on one amp and the other on the other amp is the same as an 8 ohm bridged amp.