Drivers: Linux usually supports almost everything, there was even a build of Fedora for the Nexus 7.

UI: KDE especially has very good touch screen support, including a thing that automatically changes system UI when you connect a mouse, or keyboard, or so on, and switches between phone style, tablet style, desktop with touch, and desktop style on the fly. (Essentially Microsoft’s Continuum) Since 2012.

I used KDE Plasma Active on my Nexus 7 for some time, actually.

I don't know. I suggest googling your particular laptop model, or better yet, launching a recent livecd and giving it a shot.

My touch screen works fine from my Vaio E Series to Linux Mint.