Are airports everywhere checking people's temperatures and preventing sick people from getting on airplanes?

Not everywhere: In the US and most industrialized countries, the resources are available for TSA and foreign travel agencies to test everyone for a fever. Unfortunately, in many third world countries there are not enough resources to do this. A fever is the hallmark of the covid 19 disease, but not everyone who has covid will have a fever, so there may be asymptomatic people flying in planes.