Yes it acts like luna display, but you can buy HDMI plug from third party.

The latency depends you how close you are to wifi source. When they are connected with a cable, then it depends on your local network hardware and network cards performance.

The framerate may drop if you move away from wifi or download something huge from internet like torrents, but overall it depends on how beefy the host machine is (where Deskreen app runs). My firend used a 3D modeling software Zbrush on a beefy Windows PC with Deskreen and barely noticed any lags. So it's usable even for creators.

on average it consumes pretty low network resources ~1.5 megabytes per second when watching youtube videos through it. but overall experience is good if you have fast network cards and fast router.