Solution 1:

"There" can basically be used as a substitute for an understood prepositional phrase. So you can use it in most places where you can use a prepositional phrase.

Prepositional phrases have many functions in English. They can be used to modify the meaning of a content verb, or they may be used with the copular auxiliary "be" to express a predicative meaning. There are different rules for the positioning of adverbial and predicative prepositional phrases.

Adverbial phrases may be placed after the subject and before the verb

In this case,

the infernal peers there sit in council

has the same meaning, and I think the same structure, as

the infernal peers in the palace of Pandemonium sit in council.

The prepositional phrase, or the word "there," serves as an adverbial phrase modifying the meaning of the verb "sit (in council)."

The second sounds more awkward than the first, because long adverbial phrases tend to be placed at the end of the verb phrase, but both are grammatical.

In general, there is a lot of freedom about where to place adverbial phrases in a verb phrase in English. They can come before the verb, right after the verb, or at the end of the verb phrase. (There are some rules restricting some of these options in some contexts.)

We could also say

the infernal peers sit there in council

or

the infernal peers sit in council there.

So poets can choose whichever structure sounds best.

Predicative phrases are not in general placed after the subject and before the the auxiliary "be"

However, predicative prepositional phrases (those that describe where something is, using a form of the auxiliary "be") are more fixed in position than adverbial prepositional phrases.

In normal speech, predicative prepositional phrases are never placed after the subject and before the form of "be." So "He there is" is not natural word order. It is scrambled; you might possibly encounter it in poetry, but it would be a poetic license.

The usual order is "subject - form of "be" - predicative prepositional phrase," as in "He is there" or "A fountain is in the garden." Of course, questions would follow the rule of subject-auxiliary inversion: "Is he there?"

Another order used in indicative sentences is "Predicative prepositional phrase - form of "be" - subject," as in "In the garden is a fountain."

(A third order also exists, "There he is!")