How do I know if I have a tranny problem?

I'm trying to figure out if I have anything wrong with my tranny. I know I need to replace my belts because my engine shakes a bit and there is squealing under the hood that I'm sure is coming from either the timing or the power steering belt. When my car is in reverse, without acceleration, it seems like my car is pulling, basically a grrr..and then a smooth regular engine sounding noise. It also feels like maybe there's a tension problem or maybe something else as it seems the gears are shifting at different times, or at least differently from when it used to. Are there any self-tests I can run perhaps. Thanks for your help.

Mike

stall test
time lag test
other than those two there is no further diagnosis that you can do without the trans tester that only dealers ahve.