1) If someone makes a Neder that he is going to do an Issur Mid'rabbonon does he have to do it?
2) Furthermore in Nedarim 29 it says that a child whos 12 years old and knows what a Neder is Chayov in Nedarim. According to some opinions it's Midoraisa. If a 12 year old says that hes going to do an Issur Midoraisa does he have to do it?
3) You are allowed to do a Shvus Dishvus for the need of aa Mitzvah. If you tell a Goy to do an Issur, you are Over an Issur Miderabbonon. So are you allowed to tell a Goy to tell another Goy to do turn on the light for the need of a Mitzvah?
1) The Shulchan Aruch addresses your question directly. In Yoreh Deah 239:6 the Mechaber writes: If one makes a vow to violate a Rabbinical prohibition his vow does not take effect. The reasoning behind this Halachah, presumably, is that every Isur d'Rabanan can be looked at as an extension of the the Isur d'Oraisa of Lo Sasur. And since the person is Mushba v'Omed m'Har Sinai on Lo Sasur, his vow doesn't take effect. This is how the Radbaz (commentary to Rambam, Hilchos Shavuos 1:6) explains this position. The Radbaz, however, brings another opinion that, in fact, the vow does takes effect because the Isur d'Oraisa of Lo Yachel, which is generated by his vow, nullifies the Rabbinical commandment. This latter view seems to be the view of most of the Poskim Rishonim and Achronim. The Rosh and the Rashba in Teshuvos (see Beis Yosef to Tur YD 239) say that a vow to violate an Isur d'Rabanan takes effect. In fact, this might be the opinion of the Shulchan Aruch himself.
The Shulchan Aruch, shortly before this Halachah (YD 238:4) says that if one vows to eat less than a k'Zayis of non-Kosher meat, that his vow takes effect because he is not Mushba v'Omed on less than a k'Zayis. This is quite a Chidush because the Halachah follows the opinion of R. Yochanan that Chatzi Shiur is Asur Min ha'Torah (see Yoma 74a). The Kesef Mishnah (on Rambam, Hilchos Shavuos 5:7, which is the source of the Shulchan Aruch) says that we are only Mushba v'Omed on explicit Isurim in the Torah, but not on things which are Midrash Chachamim.
Now the Shach (YD 239:20) points out the inconsistency in the Shulchan Aruch: if a vow to violate an Isur Chatzi Shiur, which is mid'Oraisa, takes effect, then surely it should take effect to violate an Isur d'Rabanan. Therefore, the Shach concludes that what the Shulchan Aruch means (in 239:6) is that, yes, the vow takes effect, but the person should not act on the vow and commit an Isur d'Rabanan; rather he should try to undo his vow. The Maharshal and the Bach (see Shach) say this explicitly.
2) The issue here is whether there is an Isur d'Rabanan on the the twelve year old not to commit the Isur d'Oraisa which he has vowed to commit. If there is, then the question reduces to the question in (1). It could be, though, that there is no Isur d'Rabanan whatsoever on the Katan, but rather there is a Chiyuv on the father and the Beis Din to prevent him from doing Aveiros. If that is the case, then it would follow that everyone would agree that his vow would take effect. Nonetheless, it would seem, that just as the Beis Din is obligated to prevent him from doing Aveiros, they would be obligated to make sure that he doesn't act on his vow, but rather has it nullified as we said above at the end of (1).
3) The Mishnah Berurah (307:24) discusses your question, bringing two opinions and concluding that in a case of great loss one may rely on the lenient opinion. The Shemiras Shabbos k'Hilchasah (I, Chapter 30, note 46) discusses a variation on your question: can one tell a non-Jew to do a Melacha d'Oraisa kil'Achar Yad? In that case, Rav Shlomo Zalman Auerbach ruled that it was Mutar. It is not clear that his reasoning would apply to your question.
Kol Tuv,
Yonasan Sigler
This is not a Psak Halachah