Hi, Teo.
I agree with Clive. They are all acceptable.
What is the grammatical term for the fronted 'clause'? I think this was once discussed here on this forum and I remember there was some controversy over the appellation of it. Some called it an 'adjectival clause,' and others referred to it as an 'adverbial clause.' I personally prefer the former, as the clause describes the subject (which is a noun)of the main clause. But those who stand up for the latter also have a valid basis for their argument, as the fronted clause originates from an adverbial clause.
As he was hungry, he decided to eat. (As....hungry: adverbial clause)
----> (Being) hungry, he decided to eat. (The sentences with this structure are often called 'participial construction.')
In participial constructions, 'being' is almost invariably followed by p.p./-ing/adjective/noun, In all these cases, 'being' is optional, but commonly omitted for the sake of conciseness.
Kind regards.
Mr. Ko