New phone

[totilele]

Charging stopping at 85% is a software choice - see https://forum.pine64.org/showthread.php?tid=12955
Jump from 40% to 14% sounds like a software bug - I've seen similar from time to time on other distros.
Charge dropping from 80% to 20% during the day suggests modem is being left fully powered - the back of the phone is probably warm a few cm below the camera. Lower power states can be used, but may have problems when waking on receiving a call, so most distros by default accept the hit on battery life for more reliable calls. The open source modem firmware project has been addressing sources of unreliability as they're found, but last I looked there remain some outstanding ones.
In short it seems about normal - some issues that have been fixed in software and some that are still being worked on but not unexpected.

The state of linux on phones is far behind laptops and desktops, largely down to stop-start availability of sufficiently open hardware and lack of resource. We've had OpenMoko, Nokia's n900, then a gap until Ubuntu briefly tried rebooting the idea (UBPorts is the leftover from that), and another gap until Purism and Pine64 came in with hardware at different ends of the price range. With each gap there's a pause in development while the rest of the world moves on, then we start playing catchup again. It doesn't help that phone hardware is a lot less standardised than PC hardware.

You may think UBPorts would be closest to Ubuntu, but they made a lot of changes to make the experience more 'phone-like' which make it rather different under the skin. The project has been concentrating on bringing their core up to date recently, and the PinePhone hasn't seen a log of progress as a result. Mobian is probably closest to what you would be used to in terms of configuration, filesystem layout and package management.
https://wiki.mobian-project.org/doku.php?id=start

Yes, I'm thinking of installing Mobian on the SD card (if I manage).
In fact, yesterday I faced another problem - somehow the phone screen started to turn on and off (like 1 second it is lighted and the keeps disappearing, if I do not keep pressing the surface. I'm not sure what the problem is.
I tried using (it's actually KDE Plasma as the internal OS) it, but it's been quite difficult.
One more problem - the Internet with SIM card in doesn't work (only with WiFi), which is again not what I want.
At the moment there seem to be so many problems, the biggest of them being not being able to use the phone because the screen keeps disappearing.

That sounds like the phone screen timeout is 0, which is also why holding a finger on the screen keeps it alive. Is that on Plasma Mobile by any chance? It used to be a bug in old releases.

yes, KDE Plasma. Strangely enough, now it works fine (just today, but no idea if that will last).
I'd like to update the system, but somehow when I see 'Updates available' it says the total size of updates is 0 ( even though it's 666 updates available).

Would recommend to update via the command line to see the actual issue, "sudo pacman -Syu".

Thank you. I've got more or less many things done, thanks to all of your support and answers. Very appreciate it. The screen timeout issue seems to have disappeared by itself somehow, now the only biggest problem is that my mobile data do not work (it actually worked for half a day and then again disappeared). 
I googled, but then I found I needed to configure APN settings, yet there are no settings listed for my country.