It depends on how restrictive the bitrate was to begin with. Higher bitrates mean there's more data to move from mini-improvements over to filling in extra resolution. Lower bitrates mean you're already squeezing every drop out and the codec will collapse when asked to handle more pixels.

Here's a couple charts: https://cdn.shopify.com/s/files/1/0095/4332/files/optimal_bi... https://di2vvsisz3gt1.cloudfront.net/wp-content/uploads/2018...

It's possible to design a codec to handle that kind of detail scaling internally, but I don't think it's been a big priority.

All else being equal, yes. The devil is very much in the details though.

It will depend on a bunch of things (codec used, encoding parameters, size of the screen, etc.), but most likely yes.