Having a ground ring tied to the oscillators ground pin is recommended by a few manufacturers guidebooks, in this case you would also tie both of the pads to ground, they do not actually connect inside, but are used to ground the case to provide sheilding from above.
Next up, I see thick nets underneath the crystal, Ideally there should be nothing other than an optional ground fill under the 2 crystal pins (1 & 3), my normal approach is to have nothing there, and another ground ring on the other side, filling it just increases capacitance, meaning you need to compensate with slightly larger matching capacitors.
pins 1 & 3 will need to connect to the microcontrollers oscillator pins,