There's no reason to use Adobe Reader for PDF files. None. PDF was made into an open standard years ago and there's many more programs that can handle them now (and render them faster, with miniscule resource footprints). Sumatra PDF, for example.
Wrong (well, except for Quicktime, but not because it's impossible). All three of those players rely on existing frameworks to handle video decoding. WMP uses Media Foundation and DirectShow (formerly/maybe still uses Video for Windows), in that order, and as far as I ever knew, the later versions of RealPlayer (seriously, why?) are also DirectShow-based. All someone needs to do is install LAV Filters and voila, Flash Video support (although getting it to take priority in WMP may mean using the DirectShow Tweaker Tool to force its merit higher).
And yes, 'Flash Video' refers to *.flv, although the name refers to two different container formats: its original incarnation is derived from SWF's container format, whereas the second form (technically, F4V, but usually still found with *.flv as the file extension) is basically an ISO Base Media file. The difference is in which formats are stored in them: anything with H.264 in it is the ISO Base Media-ish one, files with VP6 or Sorenson Spark in them are the SWF-ish one. Quicktime is also a framework by which support for extra formats can be added, but the Windows distribution of Quicktime was/is generally awful and never had the more useful components ported to it, so even if Perian or whatever successor it has now could feasibly do it, Windows users are usually left out in the cold.
Anything that uses the libraries from FFmpeg can feasibly play back almost anything. LAV Filters (and ffdshow before it) do/did this within DirectShow, Perian did it within Quicktime. VLC and the MPlayer family use the libraries standalone. All of them use libavcodec and libavformat, and sometimes the other libraries, to a greater (LAV Filters, MPlayer family) or lesser (ffdshow, VLC, Perian) extent.
I'd generally recommend any of the MPlayer family over VLC though. Preferably mpv. Those that need a GUI can use Baka MPlayer.
Oh, it does disclose it. There's no way to transmit the information without knowing where it comes from. They just don't make it easy to find the information - oftentimes it's behind multiple layers of obfuscation and cryptographic hoops incurred by the maze of files that the player VM relies on, but it is there. Otherwise there wouldn't be programs that explicitly offer direct download or playback access to the files by decoding the information the SWF layer sends, with or without the use of RTMP.
This is largely why you could have extensions for the browser replacing the web-based video players on websites (very often Flash, but not universally) with MPlayer and have it actually still work.