Question about MOSFET ground connection
Yes, the MOSFET source pins, FET driver ground and microcontroller ground are all connected. Otherwise, they wouldn't be able to drive the FETs.

Also, please be careful with that circuit. If anything goes wrong with the thing, it might catch fire or explode when it shorts out the mains. Your microcontroller will be at live voltage, so don't measure anything when it's connected. And don't leave the programming cable plugged in when you try out the circuit, it'll blow up your computer otherwise.