Dick, there are some differences in this forum and others that I frequent. A lot of it depends on what forum software is being used. As far as your questions, I can answer some of them, but I too am confused by graemlins - I don't think I've ever encountered that word in some 30 years of working with computers, much of that on the internet.
According to a google search I just did it may mean "smilies"
1) What are private messages?
These are essentially emails to other forum members that are stored within the forum.
2) What are graemlins? see above
3) What are the many ways that Watch Lists can be configured and sorted?
I'm still learning this myself (I've been here a few weeks) - apparently you can subscribe to topics or forums (which is what most forums allow) but I haven't quite worked out all the details. When you subscribe to a topic or forum you can receive an email notice when someone replies or posts to the topic/forum.
4) What are "Buddies"?
These are other members you have selected which you can be notified of their postings or simply have a friends - a clique or gang or whatever.
5) What is the maximum number for "Total topics to show per page"? (99?)
This is the number of topics to display (how far you have to scroll up or down on a single page - or how often you have to "page"
6) What is the maximum number for "Total posts to show on one page when viewing a post in flat mode"? (99?)
7) What is "flat mode"? And what other ways are there to view a post?
Generally there is flat mode -- which is just a list and there is "tree" mode which displays forums, subforums, topics as a heading, subheading, and item generally indented to group them together.
8) Here's a question to which I have yet to discover the answer: If I send a PM to a member who is accepting PMs, how can I know if he will or will not receive email notification of my PM? (I suspect that I can't know.)
I don't know that you can, most forums you don't know, just like email.
Hope that helps.