In PP CC 2017; When I extract clips from a long video, I label them and put them in a Bin but they do not appear as files on my computer. Can I assume that these are just pointers from within my Project referencing the original footage?
Elements of the Project tab (clips, sequences, black video, etc) are all abstract things which, themselves, take up no space on disk. Clips refer to media files, and those media files, of course, do take up space on disk. So, yes, you can assume that the clips in the Project tab are just pointers from within your Project referencing the original footage.
All told there is over 4 hours of video and I would like to re-assemble the scenes into various categories, such as, Holidays, Outings, Family Gatherings and Birthdays. Should I organize everything into one big project or into separate projects, like say, one for each category? Are there any particular advantages of one method over the other?
You should organize all of this as a single project, and you should create difference Sequences for each collection of clips you would like to produce as a short. For example, if "Dad's Birthday, 1945" is three different clips (we'll get to what that means in a minute), you'd make a sequence that edits together at least those three different clips, possibly with other clips that provide glimpses into the past or future.
Clips are initially the media files you import. And judging by the fact that these initial files are spliced together from shorter reels, each clip may have dozens of individual subjects. What fun! This is where you are going to want to master two things: sub-clips and Premiere Pro metadata.
Normally when shooting digitally, each time you hit the "record" button, the camera creates a digital media file that can then become a clip. Inside PPro you would then set the IN and OUT points of the clip to eliminate the unnecessary frames before and after the action you really wanted to record.
In your case, you have a clip that's a hodge-podge of recorded actions. You can select frames that constitute a specific action you'd like to use as a clip in your timeline, (right-click → Make Subclip) and it will create an object that behaves just like a clip, even though it's relative to another clip, not a media file on disk.
As soon as you make a sub-clip, it's a good idea to tag it with metadata so you can find and organize it later: categories, subjects, dates, whatever keys you can think of that will help you find, collect, and edit related sub-clips. To edit the related sub-clips, you put them into a sequence and edit.
Bins (and smart bins, which automatically collect clips according to metadata tags) can help you clean up the clutter of having 100s of sub-clips.
If you want to make 12 chapters for a DVD, you should create 12 sequences. If you want to make a monolithic DVD, one sequence will suffice. If don't initially know what you want to do, you can make sequences for each category you define. You can render "lossless" media files from each of these sequences, then import the resulting clips which you can then organize into a DVD.
To summarize: one project, sequences related to categories or chapters, rich metadata, and hundreds of clips organized into bins to keep your top-level project window sane.