As for Desktop, see my thread Installing Raspbian/LXDE on top of OSMC
Managed to setup and start a very basic Desktop (without browser & pi store & almost everything else). Still looking for a way to install the stock Raspbian browser at least.
Edit: just found out from https://www.raspberrypi.org/web-browser-released/ that sudo apt-get install epiphany-browser or iceweasel will install a browser, installing right now.