Schematic Critique - ATMEGA328P & VS1063
Can pins like CS, BSYNC, and DREQ on VS1063 be connected to any GPIO?

Yes -- this would be the easiest way of using them, and is the approach shown in the example application on page 16 of its datasheet.

Do I need the linear voltage regulators for 3V3 and 1V8? Or just voltage dividers?

Regulators.  Current usage can vary over orders of magnitude, so unless you plan on wasting a lot of power heating up your voltage divider a regulator will be necessary.

Can ATMEGA328P “B” read MP3 from SD then send data to VS1063 on the same SPI line?

Yes.  You have separate SS lines for each peripheral, so they should work just fine on the same bus.

Can I leave unused pins floating? Do I connect them to ground?

On the microcontroller, floating is fine (although I'd suggest attaching them to a pin header in case you find a use for them later).  The VS1063 datasheet states that unused GPIO pins should be grounded through a 100K resister.

Can I connect I2C lines of ATMEGAs directly?

I presume you intend to use one as I2C master and the other as an I2C slave to enable communication between the two?  This is supported, although you'll need a pull-up resister on the lines to make it work.  See the application note here.

What should I keep in mind when designing the PCB?

There doesn't seem to be anything in the design that stands out as needing particular attention; obviously pay attention to getting your decoupling capacitors close enough to the ICs they relate to, and keeping audio paths clear from sources of interference, but it should be reasonably simple design as far as I can see.