common to the c terminal

Hi All - new to the forum and would appreciate some expert guidance I would like to install a Nest to control the boiler. the old thermostat used 2 wire (R & W), which are connected to CN10 on the NHB board. I have added a blue and green wire to provide power to the thermostat but don't know...

3 wires come from the ac unit outside, 2 from the main unit. They don't seem to come together except at the thermostat except the common wire from the 24v A/C transformer. Main unit no screw terminals, just wire nutted. Here is my question. My thermostat is mounted in a main hall on a wall and...