It could possibly cause you to break out if you use it over excessively. If you just use it like once every couple of weeks, you should be fine. And it's definitely not meant for you if you have oily skin.
Do not use this on your face unless you have dry or combination skin and cleanse regularly. Coconut oil is one of the few oils that absorb into the skin so it will clog your pores (which can break you out).
It shouldn't. The coconut oil is almost a base in most moisturizer and in Chapstick, so you are getting the moister without all the added stuff. I do recommend in order to get the moister locked in just it as soon as you get out that shower.