Do I get the miztvah of learning Torah, by listening to your answers of these peoples questions?
Actually, if you do not say a correct answer out loud and only think it, then only according to the GR"A is that considered learning Torah.
Almost all other Halachic authorities hold that learning Torah requires saying the words. Therefore you would be allowed to read the answers to these questions and even listen to a shiur (Torah class) without having said Bircas HaTorah.
So I would say that if you wish to fulfill your obligation of learning Torah every day and night, do not rely on reading or even listening to any source of Torah (mi.yodeya included). Rather, take out a sefer and review something you learned over the past year.
The Mishnah Berurah(Simin Mem Zayin) says that writing is good because there is an action so I think even if you hold HIrur is no good writting would be Limmud.
If one fulfills the mitzvah of Torah study with thoughts, then Torah tapes would suffice (assuming their content counts as Torah).
This is the opinion of R. Yechiel (Avi HaRosh), Meiri, Ritva, Orchos Tzadikim, Yaavetz, Yeshuos Yaakov, Gra, and R. Ovadiah Yosef (YO vol. 4 OC 8: 17 see there for a listing of many many more who agree) (I believe it is the opinion of the Rambam as well, see below).
Rambam writes in Hil. Talmud Torah 3:14 that learning out loud facilitates memorization, whereas silent learning breeds forgetfulness.
This strongly implies that one does fulfill ones obligation to study Torah, for if not he should have said the bigger issue; that one doesn't fulfill the mitzva, rather than just saying that one is likely to forget.
R. Nachum Rabinovitch author of the monumental Yad Peshutta commentary to the Rambam, concurred with this inference.
I have found practically no Rishonim who dispute this explicitly.
However, some Acharonim such as the Pnei Yehoshua do dispute this ruling.