Initially I was able to get touchscreen working with https://github.com/onitake/gslx680-acpi driver, using firmware below, but mouse cursor was jumping around small area near pointed finger. I'm not sure whether it is a problem with touch hardware itself, driver, or not properly extracted firmware. In Windows, touchscreen is working perfectly fine and smooth though, meaning that the problem should not be in hardware. Research for a solution showed that it is possible to add some fuzz to coodinates detection, so small noise in X and Y parts is ignored. Modified driver can be found here.
Touchscreen driver needs proper firmware to be available. Firmware was extracted from Windows 10 Silead driver following the instructions from https://github.com/onitake/gsl-firmware and also this one.
mssl1680.fw is received as a result, and then converted to the format suitable for gslx680-ts-acpi driver:
./fwtool -c mssl1680.fw -m 1680 -w 1980 -h 1530 -t 1 -f track silead_ts.fw
-w 1980 and -h 1530 values are the result of experiments. Using these numers - no touchscreen calibration was required on my device.
Also note -t 1 and -f track - changing these parameters to something different causes cursor periodically jump to rightmost position.
For gslx680-ts-acpi, firmware must be put into /lib/firmware and named silead_ts.fw.
It is also possible to use silead.ko driver from Linux kernel. It still requires firmware to work properly. This one needs to be unconverted, so directly extracted file (mssl1680.fw) from Win driver is okay.
It has to be put into /lib/firmware/silead and named mssl1680.fw.
Using touch with this driver requires calibration with xinput-calibrator, and still produces small noise in cursor coordinates.
I tried both Xubuntu 16.04.2 and Ubuntu GNOME 16.04.2. They both support Wi-Fi, Bluetooth, sound, hardware buttons and backlight adjustment out-of-the-box. Touch is also okay on both, using method described above. Personally I prefer Ubuntu GNOME since its interface is more touch oriented.