Am I correct in assuming that when on 7.1 Direct the BDP-83 is doing all the processing?
Yes and no. Yes, the BDP-83 is decoding the audio. No, the BDP-83 does not have to
everything. As I noted in my setup guide, the Model 990 will provide bass management unless you have set all speakers to "large" on the 990.
How would I go about setting up the BDP-83 to use the 990s processing? Do I have to configure a separate input from the BDP-83 to the 990? Once configured as a video input I would then select the audio as "Analog" for that input?
It depends on what you are interested in. If you want to use the 990's surround processing, you'll need to use a digital audio input. That can be assigned to a video input and the 990 will do the processing, but you will be dealing with core Dolby Digital or DTS bitstreams (or stereo LPCM) instead of the lossless audio tracks offered by Blu-ray. I wouldn't recommend this approach for anything aside from CD's and DVD's.
The multichannel analog input is tied to 7.1 Direct, and it cannot be paired with any matrix surround processing. It is the preferred approach for Blu-ray, especially with the BDP-83.