Looking at getting a 4K Roku stick. It will be used for both a 4K TV that gets a 1080 signal via Spectrum cable and a 720 TV that gets a 1080 signal, again via Spectrum. A couple of questions: 1) Does this device work will with the 720 TV, or is the picture all stretched out? Also, if I am moving the Roku from the 720 TV to the 4K TV, will it automatically adjust when moved between different TVs with different resolutions?
Yes, even though the Roku device is a 4K device, it will still play on a lower resolution TV. It will simply play content in the resolution of the TV you are using.
In regards to moving the device from TV to TV, typically we don't recommend moving a device between TVs (especially if they are of different resolutions) as you may need to adjust the display settings whenever you move the device to a different TV.