I will try to answer some of your questions, but I'm not sure I can deal with all of them - I don't own the same flash.

"when would I want to reduce the power levels"
If you want to control the flash in a manual mode you can adjust flash power to match the aperture you prefer - so that you can achieve the depth of field desired. You may also want to control the power when using multiple flashes in a manual mode - one at higher power for the primary light and one at lower for a fill light. If you use the flash in a TTL or Auto mode, you shouldn't have to worry about the power - the flash and/or camera will adjust it for you (but, of course, you are then at the mercy of the programmed settings which may or may not give the results you really want).

"what does the pulse frequency do and when would I want to reduce that"
I'm guessing on this one... This may be a feature that allows capturing multiple images with a stroboscopic effect. The shutter is set for a long exposure and the flash fires several times - showing several images of a moving subject in different positions. Depending on the subject involved and its speed of movement, you may want to adjust the frequency of the repeated flash in order to capture the image sequence you are after. If it isn't this feature, then I just don't know.

"is the exposure compensation the same thing as reducing the power"
Not exactly. If I have this one correct, exposure compensation esentially tells the camera "Whatever exposure you and the flash think is correct, I want you to add (or subtract) this amount of flash from the exposure." If you find that the flash consistently overexposes or underexposes, you can use exposure compensation to adjust. Also, for instance, if you know you want a darker picture (for the mood effect) you can deliberately underexpose. Of course if you want a brighter-than-normal picture, you can do the opposite. Note that if you are using print film the lab that prints your pictures is likely to try to compensate for the over/underexposure - yielding pictures that may not match your intent.

I hope some of this helped.

Good luck,
Richard Baker

You also may want to consider buying a book or two. I would recommend "The Kodak Workshop Series: Electronic Flash" and "Flash Photograpy" by Susan McCartney

ditto ford!