I'm currently doing the glitch that allows you to catch other trainers' Pokemon, but I'm wondering if I have to grind through a lot of battles to find a shiny, or if they are predetermined. Also, are the odds different for Lv 50 vs Lv 100 or are they the same?
No, they are not predetermined. They are random just like any other shiny in the game.
Are the shinies in the BT random, and the same odds as regular shinies? I didnt really spend much time in the RS battle tower and I never saw a shiny in the Emerald Battle Frontier.
In short, yes. The reason shinies can appear in the BT is because the game references your ID and SID combo when generating them. This is normally how wild encounters are determined to be shiny or not so odds are the same (1 in 8192).
Source
This links to a shiny post on reddit of someone who caught a Shiny Dodrio from the Battle Tower Lati@s Glitch. They give directions in the pinned comment.
Hope I could help!