Recently I noticed that one wire was disconnected from oli filter, so I plugged it back to its place. Since then the oil light has been signaling low oil pressure, I guess, but only at low RPM, when idling. That is probably oil sensor, right? (I hope)

The level of oil is not the problem: I cheched that and added some.

yep or no oil

Yes, the light indicates low oil pressure.

So, you either have low pressure, or a faulty switch, or a silly wiring fault which earths the wire at tick-over.

Try new oil (15-W40 is the correct specification for the engine - cue argument about oils, again - a lot of modern oils are thinner) and filter, before the switch, as it's fairly expensive for what it is.

The bloke that taught me always said that a lit warning light proved that the bulb worked........and nothing else. If you have checked the system and it's o.k. then ignore the bulb and check the (in)famous Fiat earthing system, before spending any real money.

what is 'bulb' exactly?

The (little) lamp inside the dash

Thank you Enzo.
I'm of an age that makes assumptions, e.g. "everybody knows what a 'bulb' is".
Kindest regards,