Barak can’t be the VP candidate because he is not elibible to be president again.
The 22nd Amendment states "No person shall be elected to the office of the President more than twice". If Zer0 was VP and became president due to Biden resigning or his demise, he would become president, but not due to election as president. It may violate the intent of the 22nd Amendment, but it would not violate the strict wording.
I’d Argue based on the wording, yes he can. He CANNOT be elected President, or vice. Gerald Ford was never elected.....
Obama can be President again if nominated as VP to Replace Harris who in theory is POTUS at that moment..
The Operative term is elected.