Do I have a greater chance of getting accepted into Rice if my teacher used to go there? 
No, not at all, not a speck. That is not how college admissions works. What grade are you in? If you are a rising Jr or Sr you nee to get a basic college admissions book or spend some time reading the basics online.
Also it will help you get better answers to ask admissions questions in that forum. Chances are just guessing games.
http://talk.collegeconfidential.com/college-admissions/
lol no