Says who?
Votes must go to eligible candidates to be valid. Otherwise you could have the situation where an ineligible person is put in the Office contrary to the Constitution.
Complete nonsense. Nothing in the Constitution requires that. The Electoral College can elect anyone it wants. If the entire electoral college voted for Micky Mouse for President then Micky Mouse would be the winner. But of course Micky Mouse could not become president since he does not meet the requirements. So the presidential secession laws would kick in.
It is no different than the 2000 Missouri Senate election. Mel Carnahan, the Democratic challenger, was killed in a plane crash less than 4 weeks before the election. Due to state election laws his name could not be removed from the ballot. Come election day a dead Carnahan beat a live Ashcroft by almost 50,000 votes. In your scenario all those votes should have been disqualified and Ashcroft the loser named the winner. But instead the wished of the majority of the voters were respected and Carnahan was certified as the winner. Since Carnahan couldn't serve, being dead and all, the seat was declared vacant and the process for filling it kicked in; the governor named a replacement and a special election was held two years later. It would be the same with Obama. If he gets a majority of the electoral votes and is declared ineligible the day after the election, those votes would almost certainly remain in his name. Then the 20th Amendment would kick in and he would be replaced, probably by Biden. In any case the loser would not magically become the winner.
No the Electoral College cannot elect anyone it wants. It can ONLY elect qualified candidates. Maybe you have the US Constitution confused with the DNC wish list.
Missouri Senatoral shenannigans have nothing to do with a Presidential race. There is no Electoral College with Senatoral races.
Obama could be elected while dead but not if he does not mmet Constitutional requirements. You are not reading the 20th amendment correctly.