Comma before "and"

I understand your confusion, since the general rule is not to use a comma before "and" when you have [independent clause] + and + [essential subordinate clause].

However, in sentences 2 and 3, the independent and dependent clauses both contain a compound direct object, so it may be correct to add a comma to distinguish the clauses. The function of the comma would be to clarify the meaning of the sentence. It's a matter of personal judgment at this point, as it could also be considered correct not to add the comma. Especially if the sentences are presented in series, the parallel structure should make the meaning clear enough without the use of commas.

Although it's up to you, if the second sentence were to stand alone, then adding a comma would significantly improve its clarity. I'd suggest

Let x and y be real numbers, and a and b be integers.

and not

Let x and y be real numbers and a and b be integers.

You have four elements (x, y, a, b) that you want to divide into two groups, and each group is the direct object of a different clause of the sentence.

As a result there are four instances of "and" relatively close together and there is nothing that delineates the connection between the four elements. Adding a comma between the clauses helps to distinguish when "and" is being used to link an element to its partner from when "and" is being used to link the clauses of the sentence.

In sentence 1, only the independent clause has a compound direct object, so it's fairly clear which clause is which and how they are connected.

In sentence 3, the compound direct objects in the independent and dependent clauses are each lists of three elements separated by commas. The "and" in the lists is preceded by an Oxford comma to make it clear that all three elements are linked and are part of one unit. The commas make it easy to see that the conjunction connecting the clauses performs its own distinct function. I would argue that it's actually better not to add a comma to this sentence.