I just moved into a new apartment and everyday I am killing teeny reddish-brown spiders and very light colored (beige or almost clear) very thin legged spiders, also short, fat, brown spiders. There are also tiny ants and winged ants and the worst are centipedes or millipedes. My question is do all of these insects nest and how do I get rid of them. Help please!!

I would suggest calling a pest control professional. You also might want to check the place for any openings where these critters could be getting in and also anything that might be attracting them - holes, broken screens, food, moisture, etc.

If it is an apartment, I would also complain to the apartment owner or manager.