if you shoot manually vias through you have to name each via according to the signal - in the thermal pad case "GND".
You are missing the vias in thermal pad for the second voltage regulator..
The low profile crystal package fits under the chip..
Do use solid ground plane..
Generally : design rules - it depends on your pcb provider, most of them are checking them before the fab starts (and they shall provide you with their design rules definition, drill set definition etc..) and when they see an error they will not fab the pcb or they will charge additional fees.. :0
P.