I am running a simulation of your schematic.
1.
From what I can see, all of the M2 & M3 switches are always biased ON. However they do not conduct when their respective M1 switch is biased OFF.
2.
And i have another question about the dead-time control for the synchronous buck.
My simulation probably needs adjusting, but the waveform I see at the output has its transitions 'softened' by the action of all those capacitors. This may permit the high side to turn on as the low side is turning off (and vice-versa). Perhaps that is better than creating any 'dead time' while the coil is energized.
The reason is that the coil will want to send its energy somewhere. If it sees high impedance even for a microsecond, then your inductive time constant (L / R) becomes 8uH divided by a very high number. In one microsecond your coil could deliver a very high voltage spike.
However there is a kind of 'dead time' which might be okay. It would be the idle time when the coil has discharged completely, when running in discontinuous mode. For the remainder of the cycle the low side is On, the high side is Off.
3.
Remember that current will need to flow upward from ground, and through the low side totem pole (Mn1-Mn2-Mn3).
While you are in the development stage, for the time being it may be easier simply to install a diode pointing upward.
4.
I am not sure about the purpose for such a complicated driver network. Was this presented as the proper synchronous driver to use?
5.
I believe this network is connected to your buck converter somehow. It would help if you were to post the complete schematic.