Because video chipsets aren't all alike, this means certain required features are very hardware dependent. Since my source of information isn't unlimited, the boards I have don't cover everything under the Sun, and my time problem, you may have to wait for a future version.
If video boards were fully compatible with standard VGA, a much higher success rate would be possible.
This happens when you get beyond standard VGA modes as well. Also remember that 3D boards only AREN'T supported. The main 2D video chip is responsible for display timings, so the 3D chip just takes care of the 3D part of video. Don't ask about Voodoo support, therefore...

Yep. The Windows version can work under Windows 95/98/NT4/2000 and more than likely Millenium.

  It probably doesn't work under Windows 3.x, but the DOS version might, depending on the video driver. If the driver uses BIOS to set a mode, most likely it will work as well as in DOS on the same machine. If not, well, it doesn't! Usually it does, though.

Not on your life, pal. Have some manners first, and remember people aren't here to serve you, only because they like to help others. Be glad with what you have.

For an even more elaborate answer, read about reply #11.

When your application switches video modes, it does so usually by calling a function on your video BIOS. This function will program some specialized registers (much like variables) on the video chipset, which in turn, based on the values loaded there, will read the video memory at a certain rate, in a certain manner, and build an image which is then sent to the board's video DAC (Digital to Analog Converter), which will create an image compatible with a VGA monitor, in component (RGB, Red Green Blue) colour.

VGATV interrupts this process at the point where the application asks for a new video mode. VGATV will intercept the call, issue it by itself, but will take control of the machine before returning it to the original calling application.

After the video mode is set by BIOS, VGATV will start analyzing the current video mode and, depending on it's definition, will then readjust those registers I talk above so that the image is sent down to the DAC at a slower rate, so that the final image timing is compatible with that of TV.
This is because TV works at a different scan rate (number of complete images per second) than regular VGA, usually slower than VGA.
TV is also interlaced. Original electronics to drive the first TVs weren't fast enough to cope with the video rate, so people thought of a way to send a complete image at a slower rate, thus allowing those slow TVs to show a complete picture. The same happens on old (and not so old) VGA monitors, when they can't handle a too high resolution and/or a too high refresh rate (frames per second).
Interlacing consists of sending first the odd lines of an image (1,3,5...), top to bottom, left to right, and when the TV's electron beam reaches the screen's bottom, it returns to the top of the image and will now fill in the blank lines with the even numbered lines (2,4,6,...). So, instead of displaying a full image in a go (525 lines if NTSC, 625 lines if PAL and I think 819 lines SECAM), the TV only has to draw half of them each time, thus reducing by half the performance needed for displaying.
On the other hand, VGA is usually progressive scanned, in which the whole image is drawn top to bottom, without interruptions, reducing flicker (image tremulation). As I said above, however, when the monitor can't keep up (like those old TVs), users also have the option of turning interlace on to compensate.

After all is done, VGATV returns control to the calling application, which will use the screen just like nothing has happened. Problems may happen, though, when the application reprograms the video mode expecting it on a certain state, which it isn't anymore, thus causing the picture to become unstable, unreadable both by TV or a VGA monitor. However, these situations are rare, and only demos (multimedia DOS demonstrations ;-) and some DOS games usually do it.

Now, at this point the image is being sent down to the VGA output, completely inside TV specs. However, there are very few TVs with VGA inputs. We need to have a way to convert the component signal (RGB) into a way the TV accepts. Normally, these are composite video, where the whole signal travels together (worse quality), S-VHS or Y/C signal, where the luminance signal(Y) travels separated from the chroma/colour(C) signal, thus attaining a quality similar to RGB, and finally component/RGB video itself, for the best quality possible.
SCART/Euro-AV is a standard type of plug that accepts both RGB or composite video, or Y/C and composite video, depending on the TV (there are usually 2). This is the preferred way of connecting the VGA to TV, if recording is not intended, and the best quality is what is required. It's also very easy to interface it to the VGA card as the only electronics needed are for mixing the synchronization signals together (and I've heard you can just join the wires together and it will work, though I haven't tested it).
If you want to record your videos, animations, presentations, etc, onto video tape, you must either use composite video or Y/C (SVHS) video. As said, the SCART has a provision for Y/C, and since Y/C is about the same quality level as RGB, you may have both the good quality and the option of VCR recording. Note that getting Y/C from RGB is as hard as getting composite video, so be prepared.
Composite video is the most compatible and universal way of connecting a video equipment. It's also the hardest to get in terms of video interfacing between VGA and the TV/VCR. This is because the signal that travels completely seperated (RGB+Sync) must be mixed together into one signal only. This also introduces some artifacts, lowering the signal quality, which isn't so bad, considering that TV broadcast is done using composite video...

Hope this has been simple enough to understand.