Why doesn't Mac boot into the OS?

Hi all!

Mac won't load the OS after a sudden crash - no liquid or physical damage 

macOS 10.14.6

While watching youtube, mac suddenly froze and stopped responding to keyboard. Such things happened before and after forced shut down Mac would recover. But not this time.

After forced turn off (via power button), tried to boot it up normally - it asked password, as per usual, but never loaded completely to the OS (I didn't see the desktop).

Tried safe mode - doesn't boot it and goes to normal booting (I guess because of FileVault that is enabled).

Single user mode gives this constant string of errors, after successful password input

While booting to recovery mode, apple logo flashes red and the bar goes green, but only for a few seconds. Then goes back to normal white on black

Tried many things in recovery mode - it sees the hard drive in the Disk Utility but if I try to mount it to launch first aid, it freezes (starts heating up and spinning the hard drive like crazy) after asking for password...

Also, freezes while trying to reinstall OS in recovery mode.

And doesn't allow to make a copy of the hard drive to an external hard drive - gives this error:

Doesn’t allow launch/boot an OS from an external hard drive (asks to disable the security for that, but after entering correct password freezes and starts to heat up)

From recovery mode - doesn’t shut down if “shut down” option is picked. Only hard shut down with a button

Draining the battery completely and recharging it doesn’t help

Resetting the SMC and PRAM also doesn’t help.

Prior to the crash:

- the keyboard would double certain letters while typing (typical problem, from what I understood form your youtube vids and forums);

- occasionally would loose wi-fi connection for no apparent reason and wi-fi would start working again only after Mac restart;

- sometimes would not respond to "shut down" command (only forced shut down through the power button)

Any suggestions on what to do?

Data at the time of the crash was important, but I've kind of given up at this point... just hoping that it’s a software issue that I can fix myself with your guidance :) Or at least clue me in on what this might be.

I have taken it to a store for repair, which turned out to be proven scammers posing as certified apple repair (long story, not related to the situation), so I don’t trust their saying “full board replacement required”.