The second one, I don't think anybody says that there is no nurture component. Acknowledging theoretical possibility of a nature component via genetics is not saying that there is no nurture component, and that it does not confound any test. We would need to design better tests.
For third, that is just a definition issue. You're saying that it is wrong to investigate differences between races, but fine to do so for ethnicities. So, let us look if there are cognitive differences between different ethnicities?
Fourth is just downright false. Subgroups living in Africa are generally darker, taller, and better runners. Subgroups in east Asia generally shorter. None of the statements about physical characteristics or intelligence are about extremes or broad strict inequalities about all members. They are always statistical distributions over the whole population.
Fifth is the crux of the matter. Are we going to stop scientific inquiry because of that? Instead of trying to stop scientific inquiry, we should debate why our liberal values are useful and should hold even if there are genetic components that determine intelligence.