Which amendment prevents the president and vice president from being inhabitants of the same state? in that same amendment, who should choose the president if no one gets a majority in the electoral college? who chooses the vice president?

The admendment that prevents the president and Vice president from being inhabitants of the same state, is the 12th "...The Electors shall meet in their respective states and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves..." (Citation: The Constitution). To answer your second question, The House of Representatives, "...and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice." (Citation; The Constitution)