1. The Torah writes, "On the eight day bris milah should be performed" (Vayikra 12). Most Rishonim understand that the Torah commandment of Bris Milah must be performed on the eight day after birth, and if it is done earlier it is invalid. However the opinion of the Rosh (Shabbos 19,5) is that a bris performed before the eight day is considered valid.
2. What is the halachah? In one place the Rema (Yoreh Deah 262,1) seems to rule like leniently like the Rosh, yet in another place the Rema (Yoreh Deah 264,1) seems to rule stringently, that a bris performed within eight days is invalid.
3. Some explain that the Rema permits a milah done within eight days if it was performed by a Jew, but invalidates a milah done within eight days if it was performed by a non-Jew (Biur Hagolah, Yoreh Deah 264).
4. Most poskim disagree with the Rema (Taz, Shach, Gra, Chachmas Adam, Aruch Hashulchan, etc.) and consider a milah done with eight days to be invalid. The halachah follows these opinions, and one had a bris before the eighth day, e.g. the doctor in the hospital performed it, the bris should be repeated.
5. There is a second dispute amongst the Rishonim regarding a bris milah done by a non-religious Jew. The Rambam appears to be lenient, while other Rishonim consider such a bris to be invalid.
6. What is the halachah? While the Shulchan Aruch rules leniently like the Rambam, the Rema rules like the stringent opinions, and writes that even if the mila was already done, a small amount of blood should be removed by a religious mohel (hatafas dam bris).
7. Although one should definitely not use a non-religious mohel lechathila, a number of prominent poskim (Gra, Rav Akiva Eiger, etc.) write that if one already did the mila it can be relied on.
8. Modern day poskim (Minchas Yitzchak, Teshuvos V'Hanhagos, etc.) rule that in both of these questions one should preferably perform hatafas dam bris. However if it is very difficult, e.g. the person involved is very nervous to have blood drawn, then one can rely on the lenient opinions that the bris milah done early or by a non- religious Jew is valid. In all case a rav should be consulted.
