So, should I, can I, go from HDMI to the 990 DVI (with an adapter) then go from the DVI out with an adapter to the HDMI input of the TV, or should I just go from device to TV and let the remote handle the switching?
You can do either. If you have a single HDMI source, just run it straight to the TV. If you have two HDMI sources, I would consider using HDMI-to-DVI adapters and running both sources through the 990. If you have more than two HDMI sources, then either running all of them to the TV or through an outboard HDMI switch is going to be easier. At one point, I had a three-port switch upstream of one of my 990's DVI inputs (AppleTV, HD-DVD, and Blu-ray) and a fourth HDMI device (OPPO DVD player) on the second DVI input. That was a little extreme, though, and I still used macros on my remote to help manage input selection at the HDMI switch and on the TV (alternating between the TV's DVI input and its component video input).
You'll also want to run audio audio to the 990 separately. Depending on the device, that could be coaxial, optical, multichannel analog, or stereo analog. For Blu-ray, multichannel analog is preferred.