The adverb “already” is used not only when something is done earlier than a scheduled deadline. Another denotation of “already” is “by this time,” as in “There’s no need to preach to them because they are already converts”; no deadline is involved in that statement. A third denotation of “already” is as an intensifier of a statement, as in “Enough already, I told her last night.”
Regarding the word “being,” it actually functions in three ways: as a noun, as an adjective, and as a conjunction. As a noun, “being” has several meanings that allow it to be used not just in tandem with humans or anything related to humans; it could also mean “the quality or state of having existence,” “essence,” or “personality” of any subject other than people, as in “The Philippines being archipelagic in character, it has a coastline twice longer than that of the continental United States.” As an adjective, “being” means “present,” as in “Please stay put in your job for the time being” (it’s an integral part of the adjective phrase “for the time being”). And as a conjunction, “being” means “since” or “because,” as in “They think of him as being a traitor to the nationalistic cause.”
This being the case, the second sentence you presented is grammatically correct: “The PAWS, being the highest monitoring body on issues related to animal welfare, conducts a seminar on ‘Animal Welfare’ ...” Here, “being” is being used in the sense of “because it is.”
