I mean I guess so, letting the convention pick the VP has happened in the past (like 1956 with Adlai E Stevenson). Or party insiders could just give advise to the presidential nominee on who to pick.
Yup. VP could be chosen by the national conventions.
More interesting is the question what happens if no VP is nominated and the presidential nominee wins the election. My understanding is that the senate would chose the VP among these who received EVs for the position (usually the Top 3). If only the losing candidate gets EVs or the senate just can't vote for anyone with 51 votes, the position would most likely remain unfilled. It's unclear whether the prez could nominate a new VP under the 25 Amendment in this scenario as the vacancy was caused his the inability to elect VP in the first place and not through resignation, death or presidential ascension.
