Mazal tov on the birth of your baby!
1. Your doctor was correct in warning you that hormonal contraceptives sometimes causes light staining. These stains can make you niddah but, if the bleeding stays light, precautions can be taken to avoid this. You mentioned one such precaution: a stain found on dark underwear does not make you niddah. In our article on ketamim we review ways to avoid becoming niddah as a result of moderate staining. Please read the article, and get back to us if you have a question about any specific stain you have found.
2. Just as with a colored garment, blood found on colored toilet paper should not make you niddah, even if the stain is larger than a gris. However, toilet paper raises a different issue, which is under some halachic debate: There is a concern when toilet paper is used after urination that there might have been a hargashah (physical sensation), which renders a woman niddah. Therefore some rabbis, including the rabbi of this website, rule if you wiped within 15 seconds of urination, a stain will make you niddah even on colored toilet paper. Other rabbis disagree, and require less or no time to go by. Since this issue is under halachic debate, if you felt some time went by between urinating and wiping yourself, there is room to be lenient. If you wiped yourself immediately, you should consider yourself niddah. You are welcome to seek the advice of a different rabbi in this matter, as the advice given here is not a binding halachic ruling.
If the staining turns into a continuous flow, you should consider yourself niddah. Otherwise, keep avoiding the stains by wearing colored underwear, and try to avoid looking at toilet paper altogether. We do suggest you refrain from relations until you are sure the staining has subsided (though any other physical contact is fine, since you are not niddah).
If you'd like to provide further details about the stain you found, or if any of this was unclear, please feel free to get back to us.
3. Unfortunately, the only way to find out what birth control works for you is by giving it some time. Each woman reacts differently to the use of hormones, and you may even react differently to the same contraceptive at different times throughout your life cycle. We would suggest giving it some time before switching, as once the initial staining subsides you may discover you are quite comfortable with the pill you are on. Also take into account that your body might still be reacting to the hormonal changes postpartum. If you continue to suffer from staining, you should consult your doctor about switching to a different pill or method of contraception. if you have other medical concerns or more serious side effects, obviously you should take this up with your doctor sooner.
We wish you much hatzlachah!