Learn English – “A set of … is” or “A set of … are”

"Everybody" normally functions as equivalent to third person singular: "he pays, she pays, everybody pays".

Easiest way to build a complex sentence that uses both is to construct the subject and verb using one of the other third person singulars: "she", "he", or even "it" first, to get that part correct; "she pays ". Then build the adverbial phrase using "they", which takes a third-person plural verb: "they get", "they find", "they are", "they have". Then change "she" to "everybody", and add the adverbial phrase: "Everybody pays when they have enough money". (It's an adverbial phrase because we could replace it completely with an adverb: "everybody pays happily".)

The rule is "everybody" acts singular, "they" acts plural, and we're just accepting by fiat that "they" implies third person singular, but its actual third-person-plural nature is used to decide what verb to use.

It should be "combine with the default set A or B" in this example. If you were to have options where each choice is a set of sets, then "the default sets" would be correct. In quick, relaxed English speech, this rule may not be followed. For example, with your second sentence, any person directing crowds toward queues may say "join queues A or B," but it would be better to say "join queue A or B" as in "join the queue labeled A or the queue labeled B." I would not use "join the queue A or B," so there is some irregularity here.

A set is a singular entity, no matter how many elements it has, so the singular would be best, complete with a definite article for clarity. English speakers are used to phrases such as "combine with defaults sets A or B" in everyday speech and so this would probably remain unnoticed, even in a paper. I am almost certain both examples have been used in professional settings (not that that forbids a correct answer, but if there is an incorrect one, it is quite forgivable).

I hope this was of some help!

Edit: There is a sort of interesting thing about the word "or" in that in English, as in most other languages, it is inclusive. That is, it could also mean "and" if written without any additional quantifiers. If that is the case (if one does not forbid exclusivity), the "and" implies a multiple and would change "set" to "sets." Perhaps this contradicts the earlier parts of my answer, but it is an important nuance that comes from additional thinking on it.

So, when you say "[It] earns exactly one of the adjudications respectively of Tables 3, 4, 5 or 6." that "exactly one" is very important. This, to me, forbids the "and," thus I believe "Table" would be best. However, many English speakers may not be used to this, having the inclusive "or" on the mind at most times, and may even find it a bit unnatural to see "Table" instead of "Tables" even in this context.