I bought a rayovac portable charger. It outputs current at 800 ma/h, as stated on the product packaging. My goal here was to make my pi (model B) itself portable, as the battery outputs that current for six hours. However, I'm not quite sure how much power it draws, and definitely don't want to damage it. My question is this: Is it okay to connect a mouse, keyboard, and composite video, and power my pi from this battery pack? If not, why? Thank you.
It outputs current at 800 ma/h
I think this measurement/units are wrong. Amps are defined as Coulombs/s. So your current cannot be 800 mA/h. Your output current is 800mA. You can give a measure of the energy hours stored in the battery using a unit like A*h. But I digress...
What matters here is the output current, I think as long as you're close to 1Amp you should be fine. I have run my Rpi using a wireless USB keyboard, wired Ethernet for quite a few hrs using this battery: http://www.amazon.com/gp/product/B00BFY59BA
Using a powered USB hub for your peripherals will help prolong the run time, so your biggest power drains are gonna be from the video output and perhaps wifi if you're using it. Give it a test and see how long it runs with different peripherals feeding of it.
It may be marginal, you'll have to try and see. You won't damage the Pi (at worst if the power is insufficient you might corrupt an SD card).
There is no such thing as 800 ma/h (as noted by @cesardv)! You may mean 800 mAh, which means 800mA for 1 hour, or more likely 80mA for 10 hours (as most batteries are rated at the 10 hour rate, although this differs by battery type/construction).
If so it is unlikely to run the Pi. Check what you actually have (or post a link if you need help).