It has become common practice to refer to most meforshim by acronyms of their name (eg Rashi, Rosh, etc.). When and why did this practice start, and is it proper?
In a sense it goes back at least to the Gemara. R' Sherira Gaon points out that the names of some Amoraim that begin with ר (for example: Rabbah, Rava, Rafram) are actually shortened forms of "Rav" plus their personal name: רב+אבא=רבה (or רבא); similarly רב+אפרים=רפרם; and so forth. Also "Reish" (Lakish) is a similar short form for רבי שמעון.
I don't know when it started (or the answers to the other parts of the question), but I recall seeing "ר״מ במז״ל" in the ר״ן's commentary on the רי״ף (although that was, of course, a more recent reprint, and I don't know what the ר״ן himself wrote).
Perhaps the reason we use a shortcut when referring to their names is in order to cut to the chase and say over their Torah thoughts. The intention of this brevity is in order to show true honor to them by hurrying to say over their wisdom. The implication of this is that if one is just telling over historical facts about them that do not involve their words, spiritual level, or choices then it could be more appropriate to refer to them by their full names. I have not seen this anywhere but it stands to reason.