In regards to the 25th amendment, the president's VP pick requires a majority vote in both Houses of Congress. They (democrats) have the majority in the House of Representatives.
However, in the Senate there would be an even 50-50 (if every one stuck to party).The VP breaks the tie but if there is no VP to break the tie I don't think there is any provision for that.
tl:dr : a President can't just appoint a new VP. Congress must vote on it. But you're right that a President could nominate any one.
In regards to the 25th amendment, the president's VP pick requires a majority vote in both Houses of Congress. They (democrats) have the majority in the House of Representatives.
However, in the Senate there would be an even 50-50 (if every one stuck to party).The VP breaks the tie but if there is no VP to break the tie I don't think there is any provision for that.
tl:dr : a President can't just appoint a new VP. Congress must vote on it. But you're right that a President could nominate any one.