I fixed it. It was a parameter problem, the same mentioned in a post on PMist (apparently I can't post urls from that site but if you Google t2-qt-15-op-parameters.299483 you'll find it) with the same solution (zeroing parameters using a computer).
In my second post in this thread, some of the links don't work since PMist was switched to "cnczone". If you just switch it back to the actual website name, the urls should work.
Confused X-Axis Problem and Solution:
The x-axis was not reversed all the time (or whatever the problem was). It would try to cut from the wrong side for some operations but not all. For example, when I added another tool for finishing, for that process, the turret would try to go through workpiece to cut from the other side. Even though the control was reinitialized several times, some parameters still had asterisks in them or could not be edited. I had tried to zero the parameters using a computer, but the first time I tried, it fried my PC mainboard so I was hesitant about trying it again. Eventually, I decided to try it again with a different PC and 25-pin to 9-pin cable. I performed the procedure and it went great. It zeroed all parameters, so I didn't have to zero any parameters by hand (the ones that had to be zero, especially the ones that could not be edited for some reason such as M20 and some others in the same column). After entering all other parameters, the machine now works perfectly.
As for the eprom, I don't actually live in the US and sourcing the chips might be a bit hard or too expensive to be worth it for now. However, if and when I finish the translation and test that it works, I'll post the eprom dumps here so others with non-English controls (who want English) might benefit. In the meantime, if anyone obtains the rom dumps, it would be great if they could post them here.
I've uploaded the parameter blanking procedure I used in case anyone needs or wants it. I did it on Windows XP using a 25-pin to 9-pin cable.
Thanks to everyone for their posts.