olive oil unsaponifiables, Kim asks: Would olive oil unsaponifiables be ok for oily skin versus other oils or be considered oil free?
Technically, olive oil unsaponifiables would be considered oil free because it isn't an oil. (I've seen someone claim that a lotion with shea butter was "oil free" because shea is a butter, not an oil, but that seems like a stretch.)
Is it okay for oily skin? I don't know the answer to that question because everyone's skin is different and everyone will react differently. The only way to know that an ingredient is right for you is to try it and keep a record.
Please note that if an ingredient is causing pimples, it won't happen overnight. It can take up to a week for a pimple to erupt from the skin, so if you use something today and you've broken out tomorrow, it likely isn't the ingredient's fault. You were brewing up something under your skin and it's simply a coincidence! You may break out with something if you're having an allergic reaction, but that isn't the same as a full blown pimple!
Only you know what your skin can handle
A couple of notes on breakouts, acne, and comedogenicity