Obama is a usurper so Biden his choice is disqualified too along with all of their decisions. What has happened already cannot be changed such as all the money already spent but every other law, Presidential proclamation, treaty etc. is immediately rescinded. For the time being the Speaker of the House becomes President.
Biden ran as the VP candidate in ‘08. He was elected. It doesn’t matter WHO chose him to be that candidate.
Biden is first in the line of succession. Obama’s being declared ineligible and a usurper would fit in the category of ‘unable or unfit’ to serve. The constitutionally established succession would kick in. There is no question about Biden’s eligibility to serve as VPOTUS under the Constitution. If, on the very long shot, Obama were removed from Office, Biden would take his place constitutionally.