Hyundai i10 2009. All lights stay on when the car is in idle. All go off above ± 50km/h (31miles/h)

We have this Hyundai i10 originating from 2009.

Yes, the front seatbelts have to famous squeezing-sounds that have been reported in many similar i10 models from 2009.

However, over the last couple of months; new things started to appear.

It all started around Nov. 2023.

The ABS-light stays on after starting the car, and may or may not go off after anywhere between 10-100 kilometers (6.2-62 miles). It sometimes also lights up mid journey.

Back then, we went to the mechanic and he checked the sensors that are somewhere around all tires; all are fine.

Somehow, this small problem does **not** occur during summer.

And this has been going on since then.

But now, after the battery was replaced in Dec after it ran dead; all lights on the dashboard suddenly no longer go off after switching to ignition/starting the car.

Lights like the; engine oil pressure, high beam, the weird engine icon, seatbelt (which is only for the driver), a weird icon of a person in a car sitting, with a number 2 underneath it and above/in front of the person a circle with a cross over it, the low on fuel light and that the tail is open?

And something really odd, if I turn off the car, take out the key it starts beeping/chiming. When I close the door, it’s over. The car has automatic lights? Why is it warning me of still having the lights on?

Anyways, I need advice. Should I see a mechanic, or drive on a week or so and see if it stops or not (just like the ABS light). Is there something like a computer in there that needs a update?