Sense checking Arduino Uno barebones schematic
You shouldn't put a capacitor under the chip like that. In fact I don't much like the layout of the whole crystal circuit at all.
You need capacitors on the 7805 regulator - around 10µF on both the input and output.
The RESET pin needs a pullup resistor otherwise the chip won't function at all.
You need decoupling capacitors on all VCC pins on your main chip.
Instead of meandering ground traces you should use a ground pour.
Running from the kind of voltages you propose the 7805 is going to melt. You will need a BigAss™ heat-sink on it. For those kind of voltages you would be better using a switching (aka buck) regulator. Maybe as an off-board module to keep your board simple.