Snakes, rats, cockroaches and spiders are very difficult to kill off. If we could, we would wipe them off, but even with modern technology, we can't get rid of them, back in the past it would not have been possible.
The reference to interbreeding with neanderthals is a single DNA study, and it does not say what you think it says. It says that non-african humans share a more DNA with neanderthals than africans. The shared DNA could have come from the exit point from Africa or some other location where everyone leaving Africa passed through (like the horn of Africa). The neanderthal breeding theory is not credible at all, because the strongest overlap between neanderthals and modern humans on a DNA basis comes from the far east, where there is no skeletal history of neanderthals existing.
Might as well kill all the flowers and plants too and just make food directly from organic chemicals in processes powered by solar panels and cut living organisms out of the equation completely.
Not quite -- we simply drew down the population of Anopheles enough that malaria was unable to spread. DDT is a very effective insecticide, but resistance has been described and can spread if it is overused; in fact it is estimated that agricultural use of DDT causes more deaths from malaria by contributing to DDT resistance in Anopheles and thereby affecting vector control operations.
The reference to interbreeding with neanderthals is a single DNA study, and it does not say what you think it says. It says that non-african humans share a more DNA with neanderthals than africans. The shared DNA could have come from the exit point from Africa or some other location where everyone leaving Africa passed through (like the horn of Africa). The neanderthal breeding theory is not credible at all, because the strongest overlap between neanderthals and modern humans on a DNA basis comes from the far east, where there is no skeletal history of neanderthals existing.