Button battery is in bottom, flip it over and replace.
Nest Temperature Sensor will need to be within 50 feet (15 m) of your Nest thermostat, so they can communicate. Keep in mind that the wireless range can be reduced by walls, floors, appliances, furniture and other electronics. Take a look at this link to learn about the Nest Temperature Sensor before you buy https://support.google.com/googlenest/answer/9248154
Yes it will work. You just need to configure your nest thermostat to use the sensor on 3rd floor.
Yes, you can check the temperature remotely using the Nest app on your phone or tablet. Nest Temperature Sensor sends information to your thermostat like the temperature of the room where it’s placed. To learn more about the Nest Temperature Sensor, check here: https://support.google.com/googlenest/answer/9248154
The Nest Temperature Sensor can operate as low as 32° to 104°F (0° to 40°C). We don't recommend using it inside your refrigerator or freezer as it's designed for typical home indoor use only and is not IP rated for moisture or water proof.
Other rooms will be best effort. I just move the temp sensor around as I need it or buy more.
They only are designed to work with the Nest thermostats and pair directly with them using Bluetooth wireless and have a range of about 50 feet.
Your idea of placement sounds good. The main issue is finding a setting that allows the unit to cycle the temperature without over running the system. You would want the upstairs temperature setting at like 3 degrees above the main floor temp. Or take an average of the current temperature in each room.
See this article on google website. Each generation has a different look to it. https://support.google.com/googlenest/answer/9246551?hl=en
You can only use the Nest Temperature Sensor with Nest thermostats. Electric baseboard systems are generally not compatible with Nest thermostats. They are only compatible if they’re currently controlled by a 24V low voltage system. Please reach out to your HVAC manufacturer to verify what type of voltage your system uses to find out if Nest thermostats would work with your system.