The documents, made public in [a rare unsealing] by a secretive court panel, . . .
Yes, as you've already figured out, the phrase "a rare unsealing" is a noun phrase (NP) -- which is evident from the use of the article "a". The presence of a determiner (e.g. "a", "the") is one way of determining that. (This is a diagnostic test that can be used to help identify whether a phrase is an NP or not.)
Often an NP will be headed by a noun. But not all NPs will actually have a noun in them as its head (e.g. "Where are the sausages? Did you buy [some] yesterday?" which has a determiner-head in a fused-head construction, CGEL page 410). It so happens that in your NP, there is the adjective "rare" modifying the word "unsealing", and since:
- "Nouns are characteristically modified by adjectives, but the corresponding modifiers of verbs are adverbs" (CGEL page 82)
that seems to indicate that the word "unsealing" is a noun (which is the head of your NP) -- more specifically, that noun is a gerundial noun. (This is another diagnostic test that can often be helpful.)
There is another (3rd) diagnostic test that can be used here to help verify that the word "unsealing" is a noun: plural inflection
- "Gerundial nouns can very often inflect for plural, as in These killings must stop. This is never possible with the verbs: * Killings the birds must stop." (CGEL page 82)
and in your case, there can be plural inflection: "The documents, made public in [two rare unsealings] by a secretive court panel, . . ." -- which means that the word "unsealing" in your example is a noun.
As for your questions:
QUESTION: First of all, what does that word exactly mean because dictionaries don't seem to have this word listed in them? And could please tell me how the author came up with that word on his own?
ANSWER: There is a verb lexeme "unseal" in many dictionaries.
QUESTION: Like, what are the mechanics of creating nouns like this one out of their verb forms?
ANSWER: One way is to have that word be the head of a noun phrase, as the writer of that article had done.
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).