You do not have to be eligible to run for President. The citizens of the state’s are not electing either a candidate in the primary or the president in the general. They are giving to one person the right to send delegates to the convention or the electoral college.
In the past a lot of candidates ran as “favorite son” candidates with no intention of serving as president, but instead wishing to sway the election to favor their interests in supporting a nominee who did not get a majority going in.
The election of President does not occur until the electoral college has cast their votes and it is certified by congress. Up until they moment the question of eligibility is irrelevant. It is up to the electors and congress to make that determination. After Congress has certified the election, thereby declaring that the president elect is eligible and the election results are correct, the only way to remove the president is by impeachment. The courts have no standing before the election is certified and no jursdiction after.
Wow great analysis...here's a question...would the house certify Cruz?