There seems to be a bug in friction on wet surfaces. It requires a lot of power to get the aircraft moving. I have tested this with a couple of different aircraft and they all behave the same (pmdg 737, fenix 320). I would expect the surface to be more slippery when it’s wet. Instead it seems it is reducing braking distance rather than increasing it.
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What you are describing has been reported here:
Very nice. When is it fixed?
Never thought about that to be honest, especialy during taxiing and take-off runs.
Landing and braking on the other hand is a different cookie.
I’m not into airbusses but Boeing has a auto brake dial knob.
Off, 1, 2, 3, max.
Selecting a setting depends on runway length and landingspeed.
Not sure if rain/snow influences are (acurately) modelled in this sim.
Happy 
Airbus has autobrake.
The problem here is that there is too much friction. I would expect a plane to have less friction on a contaminated runway