This leads me to my third point, humans were evolved to be so adaptable that we survive and thrive all over the planet in all kinds of environments. We've since discovered technology to make up for our handicaps, and many diseases and disabilities do not hinder our ability to reproduce. For example, I'm very pale, and I live in a hot/sunny environment, however we have clothing and housing and sunscreen, so I'm likely not going to die of skin cancer at a young age like I might have if I had no shelter and was in the heat/sun in the desert most of my life. So, even though pale skin is detrimental when you live in sunny/hot environments, I'll still survive to reproduce (if that's the only factor we're focusing on) and pass on that pale skin gene, and it won't be naturally selected out even though it's not beneficial to my environment. It's not about "will you survive" with a certain trait, it's "will you survive long enough to reproduce." We haven't complete outgrown natural selection and evolution, but it doesn't effect us as much as it effects less adaptable species.
As for cancer, cancer covers a huge variety of diseases, many of which are caused by aging and environmental factors. You don't pass on environmental changes in body to your offspring, just like how if you dye your hair blue, your children won't be born with blue hair, if you get cancer from some environmental (which includes aging and time) factor, you're not going to give birth to children with cancer. Most cancers are just caused by malfunctions when our cells are reproducing, it can be random, environmental, or genetic. Almost all animals get cancer, not just humans, just most don't live long enough for it to be statistically significant. We just live longer than we used to and there are less things killing us than even before, so we're basically just surviving long enough to get cancer. Also, even genetic cancers usually don't take place until after we've reproduced, so we'll pass on those genes anyways. There's just so many types of cancer, each with a different cause, and most of them don't prevent us from reproducing so evolution isn't going to have much of an effect on the vast majority of cancers that plague us.