Digital Video Editing
Adobe Photoshop is the industry standard for digital photography and don't let anybody tell you anything else. Microsoft Photodraw is good but doesn't have the editing features.
"premiere" project refers to the editing application: Adobe Premiere from Adobe Creative Suite of applications.
Digital Video Editing is the process of arranging digital video footage on a timeline. The footage can come from any source as long as it is converted to digital and edited on the computer by a non-linear editing system such as final cut pro, avid, adobe premiere pro, or even Windows Movie Maker that comes with your pc. That is a really basic example. It gets far more complicated when editors start doing special effects or adding complex titles. That require the use of other programs.
It is an advanced video editing program.
Usually Microsoft Word.
Microsoft Paint works for some basic editing features.
Adobe Premiere Pro
In my opinion, the best video editing software would be Adobe: Premiere Pro CS5.
Books on editing digital video can be found in on-line bookstores such as Amazon and Good Reads. You may also find this book in the Digital Media section of your local bookstore.
DSP can stand for many items depending on the field it is used in. A couple examples are "Domain Specific Part" in computing and "Digital Signal Processor" in video editing.
An Adobe Premiere video editing project file would usually have a .ppj extension.
Adobe Premiere Pro and Adobe After Effects.