1a. In their stand-alone form, some Avisynth plugins support more than one colour space, while some are YV12 only, and you'd hope if a ffdshow filter supports YUY2 it'll be processed without converting it, but I don't know for sure if that's what ffdshow always does. The ffdshow Avisynth filter accepts YV12, YUY2 or RGB, but try typing Info() into the Avisynth filter, enable it and have a play, assuming you have Avisynth installed.
I experimented a little with an Avisynth script outputting YUY2 by opening the script with MPC-HC and using ffdshow to process the uncompressed output. I moved ffdshow's Avisynth filter down to the bottom of the filter list, enabled it and typed Info() into the text section. That get's Avisynth to display the colour space of the source, or in this case it'd be the colour space making it to the ffdshow Avisynth filter.
With only the Avisynth filter enabled and displaying Info(), Avisynth was reporting YUY2. After enabling the WarSharp filter nothing changed, but after switching to the awarpsharp version, Avisynth changed to displaying YV12, so I'll go out on a limb and say ffdshow's warpsharp supports YUY2 but the awarpsharp option does not.
ffdshow seems to output whatever it can without unnecessarily converting. For the first example it was outputting YUY2. With awarpsharp selected the output was YV12 even though the source was YUY2. If the ffdshow icon appears while it's running, hovering with the mouse displays a tooltip telling you the input and output type.
If you want to try all that I'd recommend re-opening the video with Ctrl+E after making changes to ffdshow that might effect the colour space or the output might be borked. Probably because AVIsynth doesn't expect the colour space to change.
1b. Avisynth plugins support various colour spaces. Same are YV12 only. If you try to use a plugin with an unsupported source type you'll usually see an error message and you'll have to use convert to keep it happy. http://avisynth.nl/index.php/Convert
2a. RGB conversion happens last but the output is only RGB if you disable the other candidates or a player requires it for some reason. Generally the output is an uncompressed version of the source type.
2b. I'd imagine it applies to YUY2 to RGB conversions, but it's a little ambiguous.
2c. The ffdshow debanding filter is probably designed to reducing banding already present in a video, while dithering when converting to RGB is to prevent the conversion causing banding. LAV only dithers when converting to RGB anyway, as far as I know, and usually it won't be doing so.
3. I doubt it. I assume it'd only dither when converting to RGB.
I'm not sure I'd necessarily convert to RGB in ffdshow either. Why not leave all the output options checked and let the renderer worry about converting to RGB? It's probably not going to make a huge difference either way, but EVR probably has a dither when converting to RGB, although I don't know for sure. Are you having banding issues?