Fritzing PCB design review/questions
Would this PCB work?


Possibly, sometimes, under some conditions. See below.


  Is the spacing of the board/lines to other components/side big enough?


Plenty.


  Should I use a copper/ground fill? Which and why?


For your circuit there is no real electrical reason to use a ground plane. However, many fab houses like you to use at least a copper fill in the empty areas since it means less copper has to be etched off the board, and so their etchant lasts longer before it needs to be replaced.


  Are the rounded-off traces actually better as sharp edges?


Yes. Always try to avoid right-angles. Sharp corners radiate EMI noise, mitred corners radiate a lot less.


  It says: 36mm by 15mm isn't this too small to fit all those components?


Not in the slightest.


  Can I actually use the RESET pin as other functions (without changing fuse bits)?


You can only disable the RESET functionality of the RESET pin using the fuse bits - and then it becomes somewhat difficult to program: you need a HVSP (High Voltage Serial Programmer) to get it back into programming mode again.  This blog post details how it is done.


  Doesn't it need any resistors? I've seen some on the RS485 breakout boards.


Your circuit isn't complete.  There are a couple of things missing that you need to add, and some that you might want to add.

The things that are missing:


Decoupling capacitors (100nF) on the power pins of both chips
You should have one larger (10µF typical) reservoir capacitor at the power entry to the board
(Assuming RESET is enabled) Pullup resistor on the RESET pin


The things you might want to add:


RS-485 bus termination resistors


The latter are optional depending on where in the bus your module is. You need termination resistors at both ends, so it is common to have them on the boards but with jumpers to enable/disable them.