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Since Obama was not eligible to run for POTUS, then the entire ticket is non-eligible. Succession cannot run from someone who is not eligible to be POTUS in the first place to the person who was VP on the same ticket, that reasoning goes.

This exact case is covered under the 20th Amendment. If Obama is not eligible, Biden becomes acting president. The 25th covers the case after Obama is sworn in and removed. What is not covered is the case where he is sworn in, found to be ineligible and the Congress will not remove him.

This exact case is covered under the 20th Amendment. If Obama is not eligible, Biden becomes acting president.

I'm not sure if this is covered by the 20th Amendment which states "if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified;...". No matter what Obama has been calling himself, he is not yet the president elect; that will occur when the Electors cast their votes. Also, remember that the electors cast votes separately for President and VP. IF SCOTUS decides to rule, it could become quite interesting.