So after posting this I went to a good mechanic I found - really good and honest and knows his business. He also allowed me to work on my car and just directed me and even allowed me to use a few of his tools.
He also isolated either the crank pulley or the fuel pump relay. I changed the crank...
I have an Opel Corsa 1.4 hatchback, 2002 model.
I have had some issues with the car not starting after a trip longer than 10 kms. I'd wait 20 minutes for it to cool down and it would start again. I changed spark plugs, oil, oil filter, fuel filter and that problem disappeared, but another one...