What's the purpose of the components shown in this circuits?
C2, C4, and C5 all slow down the switching edges.  These are probably a attempt at slope control.  Note that this kind of slope control lengthens the time the switching elements are kept in the transition region between full on and full off.  This can significantly increase dissipation, which needs to be taken into account in the design.

D1,R3 and D2,R4 cause the final switches to be turned off quicker than turned on.

The diodes conduct when the gate voltages are slewed up, which happens when the switches are turned off.  A forward biased diode will have roughly constant voltage across it, so the coupling from the output of Q2 to the gates has low impedance.

When the gate voltages is slewed down, the diode are reverse-biased.  This means they are in effect not there.  The resistors now couple the output of Q2 to the gates.  That, together with the gate capacitance and the extra deliberate capacitors C4 and C5, cause the switches to be turned on more slowly then they are turned on.

One reason for the asymmetry introduced by the diodes and their parallel resistors may be to compensate for the higher Q2 output impedance when driving high.  When Q2 is turned on, it actively drives its output low.  When turned off, that same node is only passively pulled up by R2.  Since values aren't shown, we can't tell if the slow rise due to R2 dominates, or the slow fall due to R3 and R4, or if they are roughly balanced.

Note that Q1 and R1 introduce yet another rise/fall asymmetry.  Q1 will actively drive its output low, which is then passively pulled up only by R1 to go high.  Again, without values we can't tell the relative strengths of these various asymmetries, and therefore which ones dominate, or whether they roughly balance each other out.