3.3V GPIO output of esp01 interfacing to CMOS logic gates operating at 12V
Is there a particular reason why you switch the high side? If you switch the low side and choose the appropriate n chan mosfet, then some of your problems go away.
Note your 1k gate resistors won’t protect from inductive kickback - that’s what the diode across the relay coil is for.
The effect of the 10k resistor and circuit capacitance should be negligible in your application as you are only switching relays.
The 1k resistor in series with the mosfet gate is called a ‘gate stopper’ to limit oscillation. Usually it is a lower value. Again, since you are switching relays, the effct on switching time is minimal as the average relay takes many millisecond to change state.