I don’t agree that Biden would become President if Obama were found to be ineligible prior to Jan 20th - he was not elected as President, and has not been sworn into office. Perhaps if Obama is degreed ineligible after Jan 20th he might become the President. I think that it is more likely that there will be a Constitutional crisis as the 20th Amendment does not cover such a situation.
I disagree. The 20th Amendment is pretty clear on what happens if the president-elect dies or is disqualified from office. One way or the other it'd almost surely be Biden.