Can I adjust the aperture of a Canon T2i while shooting a movie? I really want a greater depth of field when I'm shooting a movie.
I don't think you would want to do that, as the video you record will then get lighter and darker as you adjust the aperture which looks unnatural and is distracting. But you can manually adjust almost everything in movie mode on the t2i. Consult the manual (pg. 127) for in depth (no pun intended!) instructions.
If you want greater depth of field, then I would increase the available light and set the aperture number higher (smaller aperture). It sounds like you would also benefit from googling "Depth of Field" so you can make these decisions quickly while setting up shots in different circumstances. Your shutter speed should also be set to twice the frame rate. So, for the t2i, at 30fps, you need the shutter at 1/60, and for 24fps, you need the shutter at 1/50 (I know, it should be 1/48, but Canon does not give us that option). Good luck!