Matching stator plate with regulator - Rally 180 12V conversion

Hi

My Rally 180 engine has been machined to use a PX 200 crank, and I have this (Cosa 120W) stator plate:

https://www.sip-scootershop.com/en/products/stator+plate+piaggio+for+vespa+_23387500

I have two questions:

1. Is this the correct voltage regulator? (I have no battery)

https://www.sip-scootershop.com/en/products/voltage+regulator+effe+for_25202500

2. I see this has 4 pins - is wiring similar to the 3 pin regulators, only an extra pin available? So something like this: 12V from stator to 'G' nr 1, power to lights, horn, brake from any of 'G' 2 and/or 3? 

Thanks in advance!

Best regards
Frederik