My reasoning on the schematic is that if the circuit flows as the signal & return currents then will then it can help you visualize and layout the PCB.
If it’s broken up then the PCB gets broke up, think your circuit is a “whole” not a jigsaw.
The PSU could all run together and into the caps in 1 long run rather than 3, U1 I would put on the right of U3 and connect it up then have the RF section further to the right.
input, process, output - left to right.
Connectors showing where they are connected to without the reader having to hunt for it.
Re the GND, look at C8 and it’s GND connection, where is the other side connecting? (IC) yet the return path for that GND goes up, right, around the connector, down do C7 etc then back up to the IC in a big loop.
Instead of this big loop C8 could go directly to the IC centre pad in a short connection.
If you can now see what I mean by this, then look around the rest of the board for similar loops (I have not looked).
Vias - no there is no difference really, it’s just odd to see them as I know of no reason why they would be anything other than round (octagonal takes more room).
Caps, C4\C8 might physically be close but think about the signal that goes through them to gnd (as per the top comment about gnd loops).
If you swap C4\C8 positions you will be able to route it better.
C3 must have been a graphic thing because I have not got something turned on.
I have been playing with it but I cannot route in Eagle (IMO it’s horrid) otherwise would repost it with some differences.
Are the positions of the connectors all fixed? you have the USB top left providing power to the bottom of the board and data to the middle where if the USB was in the bottom left\middle then the connections would be shorter with less passing over the whole board.
But if your happy with the placement, I’d simply look at the connection lengths especially for the GND.
Matt