How common is the Dor YeSharim blood tests in the Dati Leumi society? I know that it is very common place in the Haradi world, that both people go for the Dor YeSharim blood tests to make sure that they aren’t carriers for any diseases. Is it common place for the people in the Dat Leumi world to do this blood test before they decide to get married?

I don’t know numbers. The Dor Yesharim testing is recommended to all, regardless to the colour of Kipa you have. An article on the subject (in Hebrew) can be found here.