The laptop is pretty unusable out of the box and suffering multiple issues. The best option is to abstain from purchasing at the moment, despite its very good nominal performance/price ratio.
1) Screen resolution
Then grub-mkconfig -o /boot/grub/grub.cfg and reboot.
2) Realtek RTL8821CE
Kudos to Vitus Wagner.
Get, build, and install the driver according to the instruction at: https://github.com/tomaspinho/rtl8821ce. You will want an Internet connection in the process (too many dependencies to carry on a drive); perhaps an Android device with USB tethering is your cheap option.
3) Touchpad click problems
It is not broken, in fact, it is just made this way: requires pressing lower part, not just tapping.
4) Screen will not wake up after suspension or blanking screen
Seems to be some obscure kernel or firmware problems. Had not enough time to deal. A workaround to disable power saving options:
Put to /etc/systemd/sleep.conf.d/nosuspend.conf:
[Sleep] AllowSuspend=no AllowHibernation=no AllowSuspendThenHibernate=no AllowHybridSleep=no
5) Minor enhancements
To provide sane console font size, put in
/etc/default/console-setup something like:
CHARMAP="UTF-8" CODESET="Lat7" FONTFACE="Terminus" FONTSIZE="28x14"
Available FONTSIZEs are 6x12, 8x14, 8x16, 10x20, 11x22, 12x24, 14x28, and 16x32.