Regarding
The Joy of Not Being Married
First, keep in mind that lots of books have titles like "The Joy of _" -- it is something of an idiom (from The Joy of Sex to The Joy of X (a book about math)...). Like most book titles, these titles aren't complete sentences: they're just stating the subject of the book, which in this case is "What Makes [Subject] Great."
The form is "The Joy of [word or phrase that functions as a noun]". So you have books like "The Joy of Cooking", where "cooking" is (as you know) a gerund (an action considered as an object, so it acts as a noun grammatically), or "The Joy of Not Working", which is about the positive aspects of retirement.
In English, "marrying" refers to the actual act of getting married. So instead the author uses "being married", where "married" by itself is a participle, a verb form that acts as an adjective. Put it together and "being married" means "the state of having a spouse" and acts as a noun. With "not," it's a book about how it's awesome to be not-married. Maybe why it's great to be single, maybe why it's great to be recently divorced, etc.
Regarding
The Joy of Not Being Sold Anything
Again, this is a variation of the stock phrase. It would also help to point out that "being sold [a thing]" has the connotation of "being subject to someone's sales pitch" or "having someone try to sell you something." (See sell definition 4). So the ad is really just saying "Isn't it nice not to have to listen to a sales pitch here? Now please buy our product."
All this discussion aside, to actually answer the question you asked: you are correct that this is a sentence fragment. That's why "to be" is absent. (As opposed to what you might be used to seeing in full sentences, something like "He is being sold a donut.")
The construction interesting to VERB implies that the person who is interested is the subject of VERB.
If I say "This video is interesting to watch", with no further qualification, I mean that when I watch the video I am interested.
If I say "This video is interesting for students to watch", I mean that when students watch the video they are interested.
Now: It is possible for VERB to be cast in the passive. For instance, if I enjoy being the center of attention I may say
It is interesting to be watched
meaning that when I am watched I am interested. And if I teach an entire class of self-centered students (which is not unlikely), I may say
It is interesting for students to be watched
meaning that when the students are watched they are interested.
But you cannot say This video is interesting to be watched, because that implies that when the video is watched the video is interested, which is nonsense—a video is inanimate, it has no feelings, it cannot be interested.
As to your final question: obviously you cannot speak of an interesting-to-be-watched video, or anything else. You might speak of an interested-to-be-watched student; that would be grammatically meaningful, but not at all idiomatic.
English really really dislikes putting adjectives in the 'attributive' position (before the noun) when they have following complements: it makes it difficult to parse the relationship between the adjective and its head, the noun it modifies. (That's why that sort of construction has to be hyphenated.) There are a few phrases which tolerate this sort of construction (easy-to-read, ready-to-wear, and the like), but I advise you to avoid it until you have a lot more experience with the language.
Best Answer
The syntactic difference, as lonehorseend points out, is that in each pair, one infinitive is active and the other is passive:
The semantic difference varies with context.
Your first pair of sentences seem to represent a philosophic recommendation, a task which you lay before everybody-in-general and nobody-in-particular. Consequently, the implicit subject of the active version is identical with the excluded subject of the passive version:
There is no real difference between the two.
This may also be true with the second pair. For instance, if you are the author of the study in question you may use either, indifferently, to announce the final task before you, your closing topic:
But for a reviewer of the study in question, the situation is quite different. The active version makes no sense in this context, because the implicit subject—the only available subject for the infinitive to mention—is the writer of the sentence: the reviewer. That would illogically make mentioning XXX in the study the reviewer's task rather than the author's.
The passive version, however, has an explicit subject, the last thing. Consequently, the clause may bear an alternative interpretation: the last thing to be mentioned may be parsed as the last thing which is mentioned. This makes perfectly good sense within the context:
Context, context, context.