Key fob not working

The very first thing and possibly the easiest would be to test the key fob. An RF tester can do this and they have them at many auto parts stores for free of use to anyone.

By the way, the key is tested and broadcasts a signal. Confirms it and light up of start stop button, when you press any of the buttons on key fob.

It sounds like the car isn't getting the correct signal. If all of your buttons are only causing the start/stop light to flash, the code is getting crossed from the fob to the cars computer. There is a guide to programming them if I remember correctly, but one of my senior experts would be able to verify that for sure. Has the key fob gotten any moisture in or on it in any way for any reason to where it may be possible your key fob may be shorted out? Not to say it would have to get wet to short out, as normal wear and tear does take its toll on key fobs as well. The next easiest step is to get a new key fob to make sure it isn't something with the car itself.

I got the car with this problem. I cannot tell you whether it's a wet key fob or not.
I tried this https://www.programyourkeys.com/BMW_1-Series_Key_R...
The problem isn't solved.

The key fob is only one, unfortunately.

I would recommend looking into purchasing a replacement fob. The big reason I would recommend this before anything else is because the problem may only be the key fob not functioning properly and since you are seeking help here, you want to attempt to resolve the issue on your own and for the solution to be as cost effective as possible. Otherwise, you will have to start looking into the BCM for the issue, which could cost you likely a bit more then attempting the most simple solutions first. Good luck and please keep us posted!