Two things to add regarding question 1:

The Steam Deck GPU is optimized for the built-in screen, which has 1280x800 pixels. FullHD is more than twice the number of pixels. The GPUs fragment fill rate will therefore not be sufficient to play many games at FullHD native. The Steam Deck has built-in FSR upscaling though, so if you are not sitting directly in front of the screen, it will look OK-ish…

The second thing is refresh rate. On the deck itself you can set the screen refresh rate to 40 Hz. For many, many games the built-in GPU will not manage 60 FPS even at 1280x800, but it quite often manages to do 40, which still feels OK-ish.

Most external screens don’t support 40Hz though, so you will be stuck with either limiting your framerate to 30 FPS, or you will have to live with either tearing or unsteady framerate.