Tanning creams just stain the skin a tanned color, so you aren't actually tanning. They come off after a few days, so you need to reapply to keep that tanned look. On the other hand, tanning creams are not a substitute for sun protection, so you still need that. Some people do get oilier as they age, though. It's a matter of genetics.
Whiteheads are a little deeper under the skin and blackheads are a little closer to the surface.
Whiteheads can lead to blackheads. They are caused by pores getting clogged up from too heavy moisturizer use, or from too much oil production from your natural oil glands on the face. Exfoliation helps refresh your skin by removing the layer of dead skin cells on top. That said, when you remove that dead layer and look refreshed, you are now more susceptible to the ravages of the environment. So you need to protect your skin with moisturizer and sunscreen, especially.