Google Nest Community

The C wire keeps the battery charged. Make sure it has power.

With the limited info you provided it would be best to check here;https://store.google.com/us/widget/compatibility/thermostat

Excellent

Before you do that I would verify the wires/colors match each connection on both ends. Double check the equipment setting on the Nest is correct. I don’t see why it won’t work.

Y1 is for cooling. Your post does not provide enough information to offer any solutions.