I am going to assume your TV is 1080p. I did not look it up. If it's not, none of this makes sense.
I also want to state a very important fact. I don't know the answer to most of your questions because every 1080p upscaling receiver is not made alike. I have no way of knowing whether any given receiver can do a better job of video processing than your TV.
I think you may have missed that point in the FAQ, because I think I mentioned it a few times. You 1080p TV MUST convert to 1080p if it's not already getting a 1080p signal. That requires deinterlacing, and scaling. These are different tasks.
You could deinterlace at the source device (e.g. a DVD player,) the AVR, or let the TV do it. You can scale at the device (e.g. a so called upconverting DVD player), you could scale in the AVR, or let the TV scale to 1080p. Pick the option that looks best.
There are AVR reviews which cover their video processing quality. But they won't compare it to your TV. So you are living with imperfect information here. I believe I discuss this in the FAQ.
1. What is the best way to connect these components via AVR?
Connect your HDMI sources with HDMI if possible. It avoids a digital to analog conversion, and an analog to digital conversion. HDMI's main downside is potential lip synch issues.
2. Is the current AVR listed above sufficient to get the best possible outcome for these components?
I don't know. I am not familiar with that model.
3. Is an AVR with 1080p upconversion necessary to get best possible picture?
1080p conversion is no gaurantee of the best possible picture. See my introductory explanation.
4. If video source is already in 1080p (blu-ray), what role does the 1080p AVR play? If it's just pass through, isn't that a waste?
5. If the video signal has already been upscaled or upconverted from the video source (i.e. playing a regular dvd on a blu-ray player), then is it necessary to still upconvert at the AVR level? If not, what would it do, pass through the video? If so how does it know what the quality of signal is?
There's no "necessary". See my introductory explanation.
6. Will a 1080p upconverting AVR upconvert my cable signal broadcasted in 1080i to 1080p? Does this mean that I can watch all my cable channels in 1080p? why or why not?
Depends on the AVR. If it can upscale you can watch in 1080p. But your TV will ALWAYS scale to 1080p no matter what you feed it.
7. What can a 1080p AVR do for vcr video? To what extent can it improve the video? All the way to 1080p? If not, is it worth it?
It MAY improve it. That's the best I can say. It could reduce noise. It could do a better job of deinterlacing to 480p than your TV. I don't know. You probably see a pattern here. I don't know, and no one else does either, because it depends on testing the specific AVR and your TV with your VCR to see if it makes a difference.
8. Is it better to send signal to 1080p AVR direct or via bitstream? What is the difference and why choose one over the other?
I am not sure what you mean. I suggest using HDMI where available, unless you run into issues. One issue would be unsolvable lip synch issues. My DVD player occasionally has the lips moving out of synch with the audio. I can correct this, sometimes by hitting stop and start. So HDMI is not perfect. In theory, it's the best option, especially for digital video sources; you would ideally not convert DVD into analog and feed it to an LCD TV, as that involves multiple conversion steps.
9. Why connect HDMI component via AVR when you can connect direct to HDTV? What are its benefits and drawbacks? Do you lose any signal quality going through the AVR?
Two reasons; audio and switching. If you don't hook your DVD/Blu-ray player into an AVR, you won't get surround sound, even if you run your TV audio back to your AVR. In general, you easily split audio and video if you choose to use HDMI. If you buy a receiver with HDMI upconversion, you can switch all audio/video using your AVR. The FAQ covers these. It also clarifies the use of the term upconverting and upconversion. They mean different things. The FAQ explains that upconversion is a confusing term because the term means something different when used for DVD players then when used for AVRs.
10. Based on my equipment, do you think I need a 1080p receiver? If yes, should I wait for the new Denon series (xx09) scheduled to release this summer? Someone recommended the Onkyo 705, but that only has a 720p upconversion, otherwise I like all other features on it including the Dolby HD, DTS Master and THX.
I don't think you need one. I do think, if you want the BEST video quality, and you have the cash, look at receivers using the Realta chip. But first you should find a review where the receiver was tested with a video benchmark, like HQV. Make sure it perform excellently in the review on a known benchmark.
11. Does an HDTV automatically upconvert or upscale all video signals it receives? If yes, then what's the point of having a 1080p AVR?
The FAQ goes into detail on this. I think I would give the same verbage as in the FAQ. So I am not sure what else to add. Short answer, because the TV may not have the BEST quality deinterlacer and/or scaler. Oppo's web sight also answers this question, you can look to see what they said.
12. Currently, on my regular TV (SDTV), some of my cable channels are not getting clear reception while others are perfect. The cable tech has been over my house 3 times and he can't improve the reception. I'v also switched boxes 3 times without success. The main cable drop is split 3 ways, with one of the lines going to my TV. Is there anything I can do to improve my signal so that all channels are clear, not just some? Could it be the splitter causing some channels to drop in quality? If yes, then how come other channels are crystal clear? I want to perfect my reception before connecting the cable to the new HDTV. Any ideas?
Blame the cable company. Not much else you can do. They are almost certainly feeding you a bad signal. My Fox used to look HORRIBLE. One big reason I replaced my Tivo with an HD model was because of that issue. The HD feed was excellent.