Yes, a VP can be charged while in office if he commits a crime of his own initiative.
However, if he acts on direction of POTUS, POTUS’s immunity extends to him...and/or every other member of the executive branch.
Biden is alleged to have sold his office coercing money from Ukraine, China and others.
If Biden’s corruption was done at the direction of Obama, he will need to prove that in court. If he proves it, Obama can be sued civilly for such sums from which he will never recover if he loses.