Sony Xperia M5: Unexpected Shutdowns during Messenger, Google Maps & Varying Battery Percentages

Hello
I recently bought a Xperia m5 phone from someone.
Unfortunately, I have already noticed a defect once in a while, 2 - 4 days, the phone turned off by itself.
Once when I was talking on the messemger with a friend and came back to the store, and the second today when I started Google maps.
Maybe you know why this is happening? Battery states different for the first time around 80% now 62%.
I don't have any Stamina modes turned on. Android 6.0 not modified.

Reload the firmware. if the thread did not change, I would start with replacing the battery anyway.

How to upload the firmware, I will add that the situation has not repeated yet

And does it have to be the same or is it going to be newer?

Added after 4 [minutes]:

Additional information, maybe not special, but important to me, I noticed that one corner of the screen is darker than the rest, it illuminates the screen less well, maybe it is the software's fault or the matrix is sitting down?

Use Xperia Companion.
Insert a picture what the screen looks like.

Phone screen brightened 100% on a white background I took a picture of my old LG LEON LTE phone, I hope you can see it.

And the question is, in this case, will my screen fall? is it the fault of the system? However, will the repair be unprofitable and I have to prepare the money for a new phone or whether this defect can remain so for a long time because in fact, at low brightness you can hardly see it and it does not bother me at a high level, because it is also poorly visible and certainly not I will return to LG Leon Lte because that phone is a failure ..


2nd question whether uploading with this program:
Xperia Companion will delete the files from the memory card again if I do not remove it?
and the third question is what system will be loaded this 6.0? older or newer?

The newest will be uploaded. You can remove the card for safety.
As for the screen, was it ok before?

From the beginning, when I bought it, I probably knew it 3 hours after buying it, because outside I was not able to see it only in a dark room or at night you can see it so much.

Added after 11 [hours] 52 [minutes]:

Now there is a problem with charging the phone
Charging with an LG charger does not bring any effects, the battery drops instead of growing additionally under a home-made powerbank, it charges normally under other chargers that I also have power drops and the computer's USB also drops.

The phone turns off again.
Recently I was running diskord and the camera was turning off (over and over).
After connecting to the charger, the problem will disappear (and recharge the battery).

Change the battery first, and then see what effect it will bring

Hi, I have not continued this topic for a long time because of the purchase and waiting for batteries
I ordered the new batteries visible in the photo
Unfortunately, the problem has not been resolved

Then I bet on the motherboard, I bought a phone with a broken matrix, but still working.
I replaced the motherboard, the problem still has not gone away, even I took batteries from this broken Sony and it did not help.
I noticed the problem that it does not occur when the phone is connected to the charger.

Maybe someone else has some suggestions to check?