Er is dependent on the dielectric material used (4.3-4.5 average for FR4 based PCBs.
Z0 is dependent on the topology used on a PCB design, number of layers proximity to planes etc etc.
Download and play with this: https://www.saturnpcb.com/pcb_toolkit.htm
Er depends on the material, nothing to do with trace geometry.
As to the rest use the Saturn calculator and observe the results, there are trace impedance calculators.
It is the ER and Zo that effect the EM wave at various frequencies not the other way round.