The only HD DVD's that will play in a standard are the Combo HD DVD's. These discs have the HD version of the movie on one side and the SD version of the same movie on the other side.
I bought a hd-dvd,jack's pov, and it plays on my Pioneer DVD-player (I don't have it here, but I don't think it is a hd-dvd-player, because I bought it about four years ago). But the picture isn't very good. It is worse than ordinary dvd. What do I need to get a better picture?
A hd-tv AND a hd-dvd-player? Or will it be sufficient with ONLY a hd-tv, or ONLY a hd-dvd-player?
I think you are confusing "shot in HD" with an actual HD-DVD disc. To play an HD-DVD disc you need an HD-DVD player and a HD TV. If a film is just 'shot in HD' that means that it was shot in high definition but lowered to standard definition for the DVD.
No, it will still play like a standard DVD regardless of your equipment. "Shot in HD" as far as standard DVD releases go simply means the picture is going to be sharper than something shot on standard video and that it will either be an anamorphic transfer or a letterboxed one. Of course it also means the studio in question can take those masters and create an HD DVD or Blu-ray if they wish...but as far as standard DVD goes, "Shot in HD" is a nice little marketing "hook" the adult studios have latched on to...but it doesn't mean a whole lot for standard DVD owners.
The way to get the most out of any standard DVD is to watch is using an upconverting DVD player connected to an HDTV using an HDMI (or HDMI -> DVI) cable. Upconverting DVD players will convert the signal to a 1080i signal (or 720p, depending on your TV). Since the source only contains 480 lines, the upconversion won't be as good as a real HD DVD. But it will be better than using a standard DVD player.
If your HDTV doesn't have an HDMI or DVI jack, don't bother with an upconverting DVD player. These players won't pass anything higher than a 480p signal using the component connections.
All HD DVD and Blu-ray players will act as upconverting DVD players when playing back a standard definition DVD.
I think I heard somewhere that a HD-TV demand special TV-air connection and HD-DVD to really get good picture, otherwise the picture looses much. Will VHS and DVD look better on an ordinary TV than on a HD-TV?
DVD's look great on HDTV's. VHS tapes don't look as good. DVD's use the full 480 lines of resolution available in the NTSC format, while standard TV uses about 330 and VHS uses 240.
It's not really HDTV's on which VHS and standard TV don't look that good. It's big TV's in general. The bigger the TV, the further apart the scan lines are. When there are fewer scan lines to begin with, they end up even further apart.
Many DVD players also have ability to upconvert the DVD signal to 480p, 720p or 1080i. It's not a "true" HD picture, but it's very good.
Higher resolution means crisper picture. The reason standard NTSC, PAL and SECAM looks os bad is because the higher resolution tends to enhance the flaws of the source. Screen size also plays a roll since the bandwidth required to maintain the same resolution for a really large screen taxes most computers (CPU/Video card) out there.