1) The resolution of a video file is written or said as just "1080".
The "i" or "p" is written or said for the player. In other words video files are always termed as 480 or 576 or 1080. Whereas in players they use the term 480i/p, 576i/p or 1080i/p. Is that correct?? Or video files themselves can be interlaced or progressive too??
The terminology is used on both ends, and it is the originating source video that matters (by far) the most. If you start with 480i video, but feed it to a 1080p display, you don't 'get' 1080p video, you get converted 480i video. On the other hand, if you start with 1080p video, and you have a 480i display, you are starting with a much higher quality source, so the final result will still likely be very good.
2) Which program can give me the complete information/properties of a video file. (Gspot doesn't tell if it is interlaced or progressive)
What type of video file? What exactly are you talking about?
Many playback programs will tell you what the resolution of a downloaded video is, and most digital downloads are progressive scan as most computer systems handle progressive scan video better than interlaced. But, then you still have to deal with video compression and different codecs as well as varying frame rates - all of which significantly impact downloaded video quality.
3) I understand that DVD standards for video resolutions are 720×480 (NTSC) or 720×576 (PAL). (i.e. 480i/p or 576i/p)
Is it possible to author a DVD with higher resolution video file and then play them in a regular DVD player??
Yes, but no.
That is, there are DVD players which play files OTHER than properly formatted industry standard DVD files. Such as DivX or WMV-HD. This capability is not part of the DVD Video specification, and is not something that a 'normal' DVD player will support. But, if your player allows for it, then you may do so. It will ONLY work in players that support that specific file format.
Otherwise, DVDs may hit a maximum resolution of 720x480i encoding. Not actually 480p, but for all intents and purposes a decent progressive scan DVD player can recreate proper 480p from the encoded material. Lower resolutions are also supported.
I have a 1080p avi file. Can I author a regular DVD out of it with the exact same resolution and then play it back in my regular DVD player??
If so how??
If your regular DVD player only supports standard DVD Video files, then no. DVD was invented pretty much before HD was around. The codecs used and necessary are not a part of the DVD Video specification and standard DVD Video players are not going to support anything higher than 720x480i video.
(BTW I have tried a lot of programs to convert a video file with resolutions higher than NTSC/PAL to DVD vob, but all of them downconvert them NTSC/PAL or below. Its as if its inbuilt in the program to make the output .vob files to be NTSC/PAL or below.)
Sounds like you have been creating standard DVD Video files. This is extremely correct for the programs to do this. If you had a Blu-ray or HD DVD player, you would be able to author a Blu-ray or HD DVD disc and put it onto a DVD as long as the file size was small enough and then play it back in one of those players with HD resolutions - no problem at all. Then the DVD is not a DVD Video disc but would be considered a HD9 disc or a BD9 disc.