Regarding point 1, the belief that the earth is 6000 years old is much more commonly held by evangelicals: Of all the major religious groups in the U.S., white evangelical Protestants are the most likely to reject evolution. Nearly two-thirds (64%) of white evangelicals say that humans and other living things have always existed in their present form, while roughly one-in-ten white evangelicals (8%) say that humans evolved through natural processes.

You can see a breakdown here: https://www.pewresearch.org/fact-tank/2014/10/30/5-facts-abo...

The rest of your argument hinges on the rejection of evolution being shared among other groups and therefore being invalid, but as you can see, the rejection of evolution is largely a evangelical phenomenon.