Piezo element microcontroller connection
R1 and C1 could be removed.

C1 protects the piezo against constant DC bias (highpass filter), but if you take care of that from the firmware, you're fine: avoid having one GPIO constantly high and the other constantly low. When mute, put both GPIO at the same level. Also, ideally, when driving, you should drive each GPIO out of phase, so the average value across the piezo is 0V.

R1 is there as the resistive element of the highpass filter created by C1. It helps discharging the piezo (which is like a capacitor) when not driven. But if you removed C1, you don't need it anymore. But it also lowers the level of the sound, so if you remove it it will be louder. 

Don't remove the diodes and R2, it protects your MCU from the spikes created by the piezo when there is a shock. But if your aim is just to make the circuit smaller, you can choose dual series diodes in a single SOT23 package like the very common BAT54S. This will make this much much smaller.