If someone who had a cut on their finger prepares your food could you get diseases from that food if blood accidentally gets in the given food?

Almost impossible: It's rare for bacteria and viruses to be in someone's blood. There are rare exceptions like Hep B and HIV; however, even if blood containing those microbes got in your food,eating it wouldn't cause you to get infected. Those microbes need to get into your blood, not your stomach (where acid and enzymes would kill them). If you had an open cut in your mouth perhaps you could get it but so unlikely!