I'll try to address your post as individual points:
- We want them to present DVD releases that accurately represent what someone would have seen in the movie theater in 1977, 1980, and 1983, respectively.
- A "negative" is what is recorded to film when it is run through the camera. This is then duplicated to make a "positive."
As an example, the left would be the negative, and the right would be the positive:
Therefore, the negative isn't suitable for projection since it isn't true-to-life colors, while the positive is. However, when the image is duplicated, quality is lost. This includes blowing up to 70mm - quality *is* lost, however minimal.
So, in order to get the most possible visual information, you would want to transfer the original negative at high resolution.
- As far as cleaning up films goes, there's physical cleanup, that is removing dirt and scratches from the physical film by chemicals or whatever else is available, and then digital cleanup, in which the scanned image is "cleaned" in the computer, which usually involves subtle alteration of the image. For instance, if a speck of dirt is on frame B, but frame A and frame C don't have dirt, a chunk of the image from either frame A or C will be copied and pasted over the dirt in frame B to "erase" it, although that's not truly what was originally there.
Then there's noise reduction. With the advent of digital cinematography, the idea of "film grain" has become associated with noise or dirt, when in reality it's part of the chemistry of the film itself and is MEANT to be there. There are methods of removing grain, but they all amount to the same thing: blurring the image and re-sharpening it, which, of course, removes detail, and can cause distortions in the image like "edge enhancement," or little halos around sharp lines (see the Episode I DVD for this).
So we basically want care taken in the cleanup process - do as much physical cleanup as is possible without causing damage to the film, then use a fine, careful touch during digital cleanup.
- Remastering. Mastering something is making a "master" copy from which to make copies. Re-mastering something is making a new master copy in a different form. So "digitally remastered" just means a new digital transfer was made, not necessarily that any careful work was put into it. It is, however, a widely thrown-around word that really has no meaning anymore.
- Restoring is, generally, making something better resemble its original version. This, too, is a term that can be used broadly. A film can be "restored" in such a way that means damage done to it over the years has been fixed, or deleted scenes can be "restored" into a film, or a film can be "restored" to its director's "original vision."
- Finally, as Ziz said, if a film was shot on 35mm, use 35mm elements to transfer it. For "Blade Runner," the film was shot with 35mm, but effects sequences were done in 70mm - for the recent "Final Cut," the original 70mm elements for the effects sequences were found and used for those sequences.
"Star Wars," however, was shot on 35mm entirely, and blown-up to 70mm the way some films are blown-up to IMAX (which is, technically, 70mm) today. When you blow something up, you distort it, no matter what. So its best to take it from the original elements, not blow-ups just because they happen to have the capacity to contain more information.
I hope I've answered your questions - it's almost 2 AM and I'm rather tired, but can't sleep.