Your placement is fine.
Your routing of the crystal signal traces is fine.
Your grounding is bad. Fortunately, doing it better actually makes your PCB design easier. There will be significant high frequency content in the microcontroller return currents and the currents thru the crystal caps. These should be contained locally and NOT allowed to flow accross the main ground plane. If you don't avoid that, you don't have a ground plane anymore but a center-fed patch antenna.
Tie all the ground immediately associated with the micro together on the top layer. This includes the micro's ground pins and the ground side of the crystal caps. Then connect this net to the main ground plane in only one place. This way the high frequency loop currents caused by the micro and the crystal stay on the local net. The only current flowing thru the connection to the main ground plane are the return currents seen by the rest of the circuit.
For extra credit, so something similar with the micro's power net, place the two single feed points near each other, then put a 10 µF or so ceramic cap right between the two immediately on the micro side of the feed points. The cap becomes a second level shunt for high frequency power to ground currents produced by the micro circuit, and the closeness of the feed points reduces the patch antenna drive level of whatever escapes your other defenses.
For more details, see https://electronics.stackexchange.com/a/15143/4512.
Added in response to your new layout:
This is definitely better in that the high frequency loop currents are kept of the main ground plane. That should reduce overall radiation from the board. Since all antennas work symmetrically as receivers and transmitters, that also reduces your susceptibility to external signals.
I don't see the need to make the ground trace from the crystal caps back to the micro so fat. There is little harm in it, but it is not necessary. The currents are quite small, so even just a 8 mil trace will be fine.
I really don't see the point to the deliberate antenna coming down from the crystal caps and wrapping around the crystal. Your signals are well below where that will start to resonate, but adding gratuitous antennas when no RF transmission or reception is intended is not a good idea. You apparently are trying to put a "guard ring" around the crystal, but gave no justification why. Unless you have very high nearby dV/dt and poorly made crystals, there is no reason they need to have guard rings.
When using Eagle's device editor, you can use 'append' to connect multiple pins to one signal. By default eagle expects all pins to be connected together, but by clicking the little icon to the left of the set of pins, you can toggle between 'all pins' and 'any pin' required for the connection.
Best Answer
Circular PCB board outlines are commonly used inside 4-20mA loop sensors and BLDC fan controllers, it's just a matter of using a circular board outline that fits inside the housing (instead of the usual "coupon" rectangular board outline). Depending on your CAD layout software, you may have to search out which layer is the "cutting" layer for defining the board outline.
Be sure to note any components that are greater than 4mm height and ensure those go towards the taller area of the housing. Essentially one side of the board becomes a "keep out" area against the taller components.
Flex PCB can work, but requires board stiffeners underneath the areas where the components are mounted. In my experience there's also some reliability/assembly issues with using flex with components mounted. Flex PCB doesn't behave quite like the usual FR4-type PCB, be sure to check whether your contract manufacturer can successfully assemble these; they're much less common.