hrm. those are tricky :)
I use a script along with lswchanger for different preferences.
The wallpapers I get (not often) I often tweak and convert to .bmp anyway...

One thing I noticed with lswchanger (my preferred wallpaper module even though it's the only one I admittedly tried) is that, along with PNG support not working, JPG support only works if you (under LS 0.24.7) set the step.rc boolean LSUseSystemDDE to be true.

So with a smattering of scripting I think it's possibly to cover #1,#2,#4,#5,#6,#7. Since my using LiteStep for so long, I don't remember what extensions explorer supports.. What are they?
As for #3, using lswchanger w/ LSUseSystemDDE, you can only have .bmp/.jpg support.

The ending syntax you want might be a tradeoff though, because of this roundabout method with scripting...

But still, using scripting you can't really do #6 unless you read from the registry the keys My Computer\HKEY_CURRENT_USER\Control Panel\Desktop>Wallpaper, WallpaperStyle
...