T or F Natural selection works to improve adaptations that increase the fitness of organisms, but genetic drift does not automatically do so?

False. There's no such thing as "(increase) genetic fitness". natural selection merely favours those traits that are beneficial in a specific environment. In many cases those same traits can be quite inconvenient in another environment.

Most famous example is sickle-cell anemia. In most environments being heterozygous for it is a problem as you have fewer functioning red bloodcells. In malaria-ridden areas it can give you an edge over people with "healthy" blood

True, because I said so.