[Static while in motion, roof mag mount]

You are starting out with a poor ground.   By using the auxiliary power connector, you can have voltage drops along with a poor ground that can introduce engine noise from the ignition and alternator.  I definitely recommend a roof mount NMO antenna.   As well as providing a better ground plane for the antenna, which will result in a much better signal, it will greatly reduce induced noise.    A 1/4 wave antenna is ok if you are local to the repeater.   However, if you do a lot of traveling or are far from the repeater, I would use a quality 5/8 wave gain antenna such as the Tram or Larson.     

[Static while in motion, roof mag mount]

I have used several Tram antennas which perform well.    If you are going to be doing a lot of traveling or are far from the repeater, nothing beats Larson.

[Can Vertex EVX-5400 UHF be used for GMRS?]

If the programming of the 5400 is similar to that of the Vertex repeaters, you can use "dealer" mode to alter the low and medium power settings to whatever output power you wish.   This would allow you to use 50 watts on GMRS, 5 watts on channels 1-7, and 0.5 watts on channels 8-14.