What is the proper behavior (by the Ashkenazi custom) during Torah reading-to sit or stand? What about the notion of standing just during Aliyot? Please bring any sources for further research into the subject.

The Talmud requires that the one who reads from the Torah stands. The Shulchan Aruch (Orach Chaim 146) states explicitely that the congregation may sit during Torah reading. The Ramah (representing Ashkenazic custom) in a gloss there says that some are strict in this regard and that the custom of Rabbi Meir (of Rottenburg) was to stand. The Mishna Brurah makes clear that even Rabbi Meir agreed that this is a stringency and that the halacha does not require standing. Further, even if one stands for the actual reading, it is certainly allowed to sit between the Aliyot. Although many people (Ashkenazim) do stand, I know many Roshei Yesiva who sit. If one's custom is to sit, there is no reason to change. The rationale for standing is to recreate the awe of receiving the Torah at Sinai, but this is in the realm of custom, and is not binding on one who has not taken on the custom.