Yes, in fact, it totally depends on the interaction between your natural level of hormones and the one that your pill will be giving to your body. So, it varies a lot from one person to another!
But, usually, if your pill has a consistant amount of hormones, then it should take approx. 1 month to be sexually fully protected.
For your skincare issue, it'll take much longer (at least 3-4 months) to be fully effective because the skin renewal process will be totally upset by the pill and it would have to adjust.
For the things you have to know, if you notice a sudden AND SIGNIFICANT weight gain or loss, go ask your doctor, he/she might have to do another blood test!