2. In LXDE tapping the screen will always trigger the right mouse button which makes it hard to control the desktop. I guess that's manageable via evdev. Reading man evdev also revealed that tap-hold for right click can be configured via evdev and therefore desktop-independent.
$ find /dev/input/by-id/ -name "*event-mouse" /dev/input/by-id/usb-Logitech_USB_Mouse-event-mouse
$ ls /dev/input/ by-path event0 event1 event2 event3 mice mouse0
4. LXDE battery monitor may not work. I say "may" because I only tried with power cable connected.
I didn't try phone functions so far, but I'll try soon. Unfortunately the fso-deviced package isn't installable on i386/amd64 atm. Not sure if it's any better on armhf.