That is actually not true. If your AppleTV has tvOS 9 or newer, you can activate P2P AirPlay. It’ll create an Ad-Hoc network only between your TV and Mac/Phone and use that for AirPlay, no further network or internet connection necessary. You just have to activate it in your AppleTV settings.
Edit: Alternatively, the Hollyland Mars 4K is a pretty decent wireless video transmitter that supports HDMI, that I’ve used in a professional setting sometimes. Not sure it is what you’re looking for (or sensible, price wise) but you probably won’t get a more stable connection with anything cheaper.
Could be bromine. It’s a reddish brown liquid that’s highly corrosive and toxic and is typically fused into ampules for storage, as it gives off toxic fumes.
Be careful to not break it or get it too warm until you know for sure what it is.