By late antiquity, the "beth midrash" had developed along with the synagogue into a distinct though somewhat related institution. The main difference between the "beth midrash" and "beth hakeneset" (synagogue) is that the "beth hakeneset" is sanctified for prayer only and that even the study of Torah would violate its sanctity while in the "beth midrash" both Torah study and prayer are allowed. For this reason most synagogues designate their sanctaury as a "beth midrash" so that in addition to prayer the study of the Torah would also be permitted. http://en.wikipedia.org/wiki/Beth_midrash
Why does Torah study violate Beit Kneset sanctity unless otherwise specified (i.e. when Beit Kneset is a Beit Midrash) and which Halakhic rule applies to this situation?
In times of Yavneh, Torah study was the ultimate form of worship, so is it not so anymore? Of course, it is - Torah is read during the services, also Torah is usually available in printed form for every attendant of the service so reading from this printed Torah (and thus hypothetically not paying respect to the Sefer Torah) must not be a violation then. I know in old shtetls in Europe there was always a table to study and explain Torah in a Beit Kneset - it was so 100 years ago, but not anymore. And it is written learned prayers and rituals if executed without analysis, without giving one's heart to it, are wrong and without effect.