I agree - I would crank up your VCC and GND lines, as you have plenty of space. I think with the 7-8 mil tracks you can draw about 800 mA on 1 oz copper, it's probably fine, but just for the sake of it
Yes, that might be a good idea... However, here is a question. In my understanding, the effective width of a track is determined by its narrowest part / segment, and that is already determined by the connector pin as well as the leads within the CPC going to the edge connector. How can a thicker / wider track make any difference if the narrowest part is before that segment? Also, the connector pin will have poor conductivity as well.
So, I think there are certainly good design patterns and best practices, including
- backside copper GND plane
- decoupling capacitors for each chip
- large width of tracks etc.
but I doubt that these are really strictly necessary for the current, voltage and frequency ranges the CPC operates at. Just my 2 cents

I am probably wrong though.