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.
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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.