One Non-Finite Clause as a Subject? Singular Verb
To study this question more closely, I went to the News on the Web (NOW) Corpus, ran a search for "Being rich and famous" (139 results). Out of the results, when the non-finite clause was a subject, every verb was singular. Here are some examples:
Being rich and famous is not a marker of success
Being rich and famous comes with a few unexpected downsides
Being rich and famous awards you a fair bit of wiggle room
In each case, the non-finite clause (ones headed by an infinitive or participial form; see Wikipedia) takes a singular verb, even if the clause has multiple or plural elements within (see Celce-Murcia, Larsen-Freeman, Williams, The Grammar Book, p. 66).
Two Non-Finite Clauses as a Subject? Usually a Plural Verb
Take this example:
Being rich and being famous are sufficient for Bob to be happy. (Causey, Logic, Sets, and Recursion, 2006).
In this case, two nonfinite clauses connected by and are treated as plural rather than singular. That would govern both your second and third examples.
This construction is unusual though; I wouldn't be surprised to see a native speaker say something like
Being rich and being famous is sufficient for Bob to be happy
because they think of it in a singular mode or pertaining to only one entity (Bob), a form of notional agreement or determining agreement by meaning. (For more exploration of those possibilities, the question "Singular vs. Plural with Multiple Gerunds as Subject (IE: [Gerund] and [Gerund] are/is [something].)" explores some possibilities).