Question: Can I fulfil my obligation of shnaim mikra by reading the Chumash along with the baal korei? Can I read the Rashi in English?
Answer: The Shulchan Aruch (OC 285:1) writes that even though one listens to the Torah being read on Shabbos, one must review the parsha twice each week together with either the Targum or Rashi (See Berachos 8a). The Mishna Berura (285:6) explains that they each have advantages over each other.
There is a machlokes as to whether listening to leining counts as having read the Torah once. The Magen Avraham (OC 285:8) and Chaye Adam (7:9) write that it does, while Rambam (Tefilla 13:25) and the Beis Yosef (OC 285) holds that listening does not help.
The Shulchan Aruch (285:5) writes that reading (quietly) along with the baal korei counts as reading the Torah (See Aruch HaShulchan OC 285:3 quoting the Perisha).
The Mishna Berura (146:15) quotes differing opinions as to whether it is more appropriate to follow along silently with the baal korei or to read the words to oneself, though elsewhere (285:14) he writes that one can read along if one wants to fulfil one’s obligation of shnaim mikra. R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 42:58) writes, though, that if one does have the time, it is best to do so before leining.
R’ Ovadia Yosef (Yechave Daas 2:37) and R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 42:n215) write that even if one doesn’t understand the Targum properly, they should still read shnaim mikra.
The Mishna Berura (285:5) writes that one who doesn’t understand the Targum or Rashi can read the tz’ena ur’ena (in German) instead (See Taz OC 285:2).Thus, R’ Moshe Sternbuch (Teshuvos Vehanhagos 1:261) writes that if one doesn’t understand the Targum one may read shnaim mikra together with an English translation of Rashi.