If someone can provide the grammatical terms related to my question it would be greatly appreciated as I was uncertain of what search phrases would apply.
Perhaps search on "extraposition" (and maybe also predicative complements). An extraposition construction has one more position in it than the corresponding more basic alternant.
Your second set of examples seem to be using extraposition, which involves the process where a subordinate clause is moved to the end and then the subordinate clause's original location is then occupied by the dummy pronoun "it".
I'll bracket the involved complements in your two examples, and bold both the dummy pronoun "it" and the relocated (extraposed) subordinate clause:
Those two examples have the same meaning as the following two simpler versions, which don't have the extraposition, and which happen to be ungrammatical:
Notice how the bracketed complements form an (object) predicand and predicative complement pair. That is: "to go sailing" is "a good idea", and "to dress like a pirate" is "appropriate".
The predicands ("to go sailing" and "to dress like a pirate") are non-finite clauses -- in this case, they are infinitivals. But an infinitival cannot occur between a verb and a predicative complement (page 1255, CGEL); and so, normally, the infinitival is extraposed. And that is what happens and results in your two versions #1b and #2b.
Compare your two examples to examples that don't involve a subordinate clause:
For predicands that are noun phrases, extraposition is generally not an option:
Those above two examples are ungrammatical.
But in examples like those in the OP's original post, which involved infinitival clauses in the object predicand location, extraposition is obligatory.
EDITED-TO-ADD: Your first pair of examples uses a declarative content clause:
which also uses extraposition, where it involves the subject of a content clause. That is, the more basic alternants for the content clauses are: "to go sailing was a good idea", "to dress like a pirate was appropriate".