The rule is that one is not allowed to kill two birds with one stone with tzedaka. In other words, one cannot use tzedaka money to fulfill mitzvot that he is obligated to do independent of the mitzva of tzedaka (e.g., buy a lulav and etrog, support his wife).[1] One may, however, receive indirect benefit (honor, debt of gratitude) from his donation.
Matanot la’evyonim is an independent obligation, halachically distinct from tzedaka (even though there is a strong philosophical connection) and thus, should not counted toward giving ma’aser. Since it is sufficient to give to two poor people, once that has been done, one has no further obligation. If he wants to give more, he can deduct the additional money from ma’aser.[2] By doing so, he would not be fulfilling (with the additional ma’aser money) the special mitzva of matanot la’evyionim but, rather, regular tzedaka that happens to be given on Purim, an auspicious time for tzedaka as well.
Regarding kaparot, Sefer Tzedaka U’Mishpat[3] rules that since it has been accepted as an obligation, ma’aser money should not be used. As far as tzedaka before Shabbat is concerned, it seems that those who have this practice did not accept it as a new obligation, but simply as an auspicious time to allocate tzedaka. It is probably best that one who resolves to start this practice have in mind that he will take the funds from ma’aser (if that is what he wants). However, even without such a stipulation, the money given to tzedaka before Shabbat can be counted toward ma’aser. There are several good new books on the topic of ma’aser kesafim that discuss, among other things, whether certain payments are independent obligations or can be taken from ma’aser.
Regarding your assumption about the maximum amount of tzedaka, one is, in fact, allowed to give more than 10%. The limit is 20%,[4] while 10% is considered a positive, average rate of charity. What you may have heard is that it is proper to make an accurate calculation of 10%, as opposed to giving more without calculating.[5] However, if you calculate and put the money aside, and then decide to give more as regular tzedaka (or don’t count certain donations toward ma’aser, which comes to the same thing), that is wonderful.
May you always have the desire and resources to fulfill the beautiful mitzva of tzedaka in its various forms.