Is "Being socially responsible", a prepositional phrase?

No.

"being" is a participle, a verb form

Read and study about prepositions and prepositional phrases:
http://www.chompchomp.com/terms/preposition.htm
and
http://www.chompchomp.com/terms/prepositionalphrase.htm

Yes, "Being socially responsible" is a participial phrase, not a prepositional phrase. Participial phrases are made up of a present or past participle verb along with any modifiers or complements. In this case, "being" is the present participle form of the verb "be," and "socially responsible" are the modifiers describing the subject of the sentence or phrase.

Yes, "Being socially responsible" is a prepositional phrase.