MacOS High Sierra restarts every 10 minuts without any warning sign

Well, if it comes to that, here's what you can expect:

Note: I have been buying Apple computers since the nineties and would never consider not getting AppleCare. It's saved me on several occasions.

There is also the chance that they may still cover the repair, but you won't know until you take it in.

I would run a full RECOVERY and Reinstall your system !!! Now, there's NO use waiting if it's doing this in SAFE MODE & Single User but not Recovery - Take the golden goose egg and run!

Just curious - HOW exactly did you do your 'Re-Install' ?

Can anyone suggest what might be at fault/where to look to diagnose the actual fault?

It is nearly certain to be a hardware fault that only Apple will be able to definitively diagnose or fix. You already took all the appropriate steps to eliminate other causes.

Contact Support

Determining exactly which hardware component or components are involved is not easily accomplished, but if you wish you can use the following short Terminal command to identify the numeric "shutdown code" involved:

log show --style syslog --last 96h | egrep shutdown\ cause | awk -F')' '{print substr($0,1,19), $NF}'

Copy (position your cursor in the above line and triple-click to select the entire line) and Paste that entire line into a Terminal window.

After a few moments it will return something like this:

iMac4:~ john$ log show --style syslog --last 96h | egrep shutdown\ cause | awk -F')' '{print substr($0,1,19), $NF}'

2017-12-10 07:07:15 Previous shutdown cause: 5

2017-12-10 21:11:53 Previous shutdown cause: 5

iMac4:~ john$

The meaning of those codes is not publicly documented, but some of them are commonly known. What is that numeric code?

Note: log is not present in Yosemite. If that's what remains installed you need to use another method, which I can describe if needed (summary: launch the Console app and type shutdown cause in its Filter field).

Make an appointment with the Genius Bar. It is most likely a faulty battery. They have the ability test for battery problems beyond anything that is going to show up in the System Report.

I also have an Early 2015 12" MacBook and its battery failed around 300 something cycles. The battery was replaced under AppleCare.

I can only speculate regarding the exact cause, but the symptoms you describe are consistent with a faulty battery. They're not terribly expensive to replace, and for all I know Apple may be aware of a problem they are not willing to discuss publicly.

In any event they will be able to provide a definitive diagnosis and repair options, probably at no charge.

What I'm afraid of is, they are known for replacing entire lower/upper half of the laptop for minimal faults in some modules.

I know. Some repairs are not economically justified. Some things can't be fixed at any price. Other things could be free. You won't know until you ask.

Actually unless you've run this you do...

Your code is usually associated with:

-60 bad master directory block, serious disk error

BUT

Sometimes a FIRST AID from disk utility

OR fsck from SAFE Mode

and a Reset SMC does the trick

I can't see the thread - but I believe you got a hardware probable -60 code, right ?

Are you still getting these codes on the latest reboots?

log show --style syslog --last 96h | egrep shutdown\ cause | awk -F')' '{print substr($0,1,19), $NF}'

Very possible either CLEAN install or a repair situation of a drive or some component is your next step.

2017-12-15 12:08:05 Previous shutdown cause: -63

When not associated with a predictable event (a firmware update, for example) negative shutdown codes indicate a hardware fault: Contact Support.

Also, please note that the initial estimates were higher than the actual charges, $575 down to $280. Compare this initial work authorization to the final one given above.

Technically, the battery replacement, if required, is done by replacing the bottom plate assembly.