Formerly, your Nest worked by leaking power through the furnace or air conditioner's operating relay. The relay was old and brutish enough that it flowed enough current for it to work. Now, you have an electronic control furnace that does not have those smarts. This is similar to the problem people have with lighted switches or dimmers when they switch ...
The thermostat is simply pressed onto the mounting bracket and "snaps" into place.
See the installation guide or Carrier's video; at ~2:20, it shows the thermostat being mounted.
Since there is no description for removal, I'd try prying gently along the four edges, between thermostat and wall.
BTW, the owner's manual omits mounting the device.
Yes, that C connector on the valves is what you want. The nest thermostats use very little power, so that shouldn't be an issue for your transformer.
There are two wires coming from the transformer. On a typical HVAC system, the red wire is used for control, and the other wire is what gets used as the "common" or C-wire. In your diagram it looks like ...
In the vast majority of jurisdictions, most DIY work is perfectly legal in a house you own/land contract, and live in. The only exceptions are things like Freon handling, gas lines, and several other crafts, due to the particular hazards (often indirect, e.g. Freon).
You're not allowed to work on houses you don't own for obvious reasons. In many crafts, ...
The final answer will depend on your specific jurisdiction. However, generally speaking
Plumbing - gas and water - typically requires appropriate licensing and/or permits
Electrical - "mains" voltage or above - i.e., typically greater than some particular voltage, but generally designed to include 120V/240V (and above) but NOT to include telephone, network, ...
The thermostat doesn't actually have a way to check your filter to see whether it is clean or not. The flashing "filter" turns on based on time - every 3 months. Resetting it (look in your manual) will make it start flashing in another three months.
You can't get there from here
That thermostat simply will not work in that location. The wiring to that thermostat is wired as a switch loop.
This is the 240V version of "no neutral wire in the switch box, so no smart switch".
Back to the store it goes. They probably get 30% of them back this way.
Go 24V system
Fuel furnace thermostats run on 24 ...
You should be able to use that screw terminal for the C wire in the bottom picture. I assume that the blue wire on the spade terminal goes to the 24v transformer? It looks like the transformer has a red wire and a blue wire coming off it. The red wire from the transformer is the "R" and the blue wire would then be the "C" wire.
Looks like an easy hookup -...
I think you are right. From what I remember once I did something similar as their was no c to the thermostat. Luckily for me the unit was right next to the thermostat so it wasn’t hard to run.
You could use this instead if you don’t want to run the cable?
Venstar ACC0410 Add-A-Wire Kit https://www.amazon.com/dp/B008PLWT8C/ref=cm_sw_r_cp_api_i_OFbeDbAE61VDQ