As already answered in your other thread brown is simply old blood, it is normal it does happen to all women at some point.
Birth control works within a week or but doctors say as a precaution to treat that as a month by using a condom as well so that you are used to being careful in the first place. As long as you have been taking it on time like you have been then the pill is already working as it should.
Spotting is absolutely normal when you start the pill, says so in the instructions (they are long in the pill box it came in but it will answer a lot of questions), and spotting can occur at any point in the cycle meaning active pills or placebos. It can also occur for up to 3 months or more as your body is still getting used to seeing the pill there. Everything you are experiencing is normal, it does not mean you are pregnant. Another thing would be that missing a pill by more than the 3 hour window DOES NOT mean you will become pregnant. Getting pregnant while on the pill is extremely difficult, the pill is about 99.7% effective when taken as directed every day no missing skipping or losing pills and so on. Getting pregnant on the pill means astronomical odds were beat or the woman simply is no good at taking the pill when they should hence losing the effectiveness of being on the pill. You are taking it as you should when you should so you are taking it correctly, having a common side effect like spotting does not absolutely mean you are pregnant.