I use traditional, standard English grammar, and this might help...
I found Berhman in his room helpless with pain and fever.
This is a Simple Sentence with one subject "I" and one verb "found."
"found" is a transitive verb and takes an object, here, a direct object: Berhman.
The verb "found" is modified by an adverb prepositional phrase "in his room" to answer what an adverb would ask, "Where?" Where did you find Berhman? In his room.
The preposition phrase consists of the preposition "in" a possessive pronoun "his" and the object of the preposition (a noun or pronoun) "room."
An adjective doesn't always have to come right next to the word it modifies, so "helpless" is just that an adjective modifying "Berhman."
e.g. I found helpless Berhman in his room with pain and fever. [sounds awkward, hence, it's placed later in the sentence]
The adjective "helpless" simply means "without help or defense" and is being modified to by the adverb prepositional phrase "with pain and fever." The phrase answers, "To what extent?" To what extent was he helpless? Pain and fever caused him to become helpless more or less.
The objects for the preposition "without" are "help, defense" [both nouns]
But I am somehow confused with this sentence, choosing between
"Berhman in his room" as the object of "found", and
"in his room" as the adverb of "found".
You are correct on both.
Again, Berhman is the object (direct object) of found.
in his room is the adverb modifying found.