Does changing my bridge affect my guitar's tone? And will it make palm mutes sound good? I want to change it to a Floyd Rose Ibanez bridge.
Bridges with different vibrato systems will vary in terms of tuning stability, range of pitch variation, and response of the bar itself. Bridges also vary in terms of the range of set up they allow, and the ease with which adjustments can be made, strings can be changed, and so on.
However the effect of the bridge on the timbre of the guitar is likely to be very small, assuming it is properly installed and set up. It will be especially small when palm muting, because the damping of the string with the hand reduces the vibrations that are transmitted between the bridge and the part of the string where the pickups are.
The only reason to consider changing a bridge to help your palm muting would be if your current bridge is somehow interfering with your technique. Changing the bridge will probably make little or no noticeable improvement to your tone.