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It seems that "Here" is only an adverb. That means it has no other part of speech except an adverb.
here is/are something (also here it is/here they are)
a) used when you are giving something to someone, or showing something to them (source)
Ok, let see this conversation
A: could you give me the pen?
B: Here is your pen / Here it is
Can B reply "Here is it"?
It sounds pretty strange when saying "Here is it".
A: Could you give me the pen?
B: Here is your pen / Here it is
No: B. cannot reply *"Here is it" because subject-auxiliary inversion would be wrong here.
B’s responses "Here is your pen" and "Here it is" are fine and exhibit subject-dependent inversion (the normal order would be "Your pen is here" / "It is here").
But the act of preposing "here" to the front of the clause does not trigger subject-auxiliary inversion, which answers your question about why *"Here is it" is wrong.
Incidentally, traditional grammar analyses "here" as an adverb, but some modern grammars analyse it as an intransitive preposition contrasting with locative "there". In your examples, "here" is being used deictically, and it accompanies the act of presenting the pen to A.
The basic sentence is
It is here - subject-verb-adverb
With adverbs, there is some latitude on positioning, and it is normal to move the adverb to the start of the sentence for emphasis, like this:
Here it is!
If you invert the order of the subject and verb, that makes it into a question:
Is it here?
If you then move the adverb to the front for emphasis, it's still a question, albeit a rather unusual one:
Here, is it?
When the adverbs "here" and "there" are used at the beginning of a sentence, they can cause full inversion only when the subject is a noun or a noun phrase other than a pronoun. Notice the difference:
Here is your book / Here it is.
There goes my train / There it goes.
Here comes Mary / Here she comes.
Note: The way this is expressed in the dictionary you quoted (here is/are something (also here it is/here they are)) is confusing, since both forms are not interchangeable. Notice, however, that the examples in the dictionary follow the rules I mentioned above.
