Sounds like it's a quick primary? So will VPs be picked before the nomination is finalized? Can multiple candidates pick the same VP? If after the nomination, it has to be pretty fast. Pick the second place finisher?
The person who is chosen for President will announce a decision. How much influence others have over that decision is unclear, but officially it is the decision of the Presidential nominee.
The process for VP selection is handled by the Presidential candidate and usually takes months. For instance, McCain started steps in his VP selection around Memorial Day for an announcement in late August. Even then, he made a last minute change to consider Palin, which ended up with Palin not being fully vetted.
Harris is really behind in the selection process, not even having a committee to advise on selecting who the VP candidate should be.
As this primary didn't have serious competition, I don't think she will select the second place finisher.
My money is on Pete Buttigieg because it will represent a continuation of the administration, he's gone through the vetting process to run for President, and he's been able to conduct himself well in national media.
Governors carry the risk of not knowing how to deal with national media. Senators are needed in the Senate and also may not have that full experience. House members aren't usually picked.
Don't expect a VP before the convention and the president is decided. Do expect that the VP will be from MI or PA as the boost there would make this a very difficult run for Trump.
Maybe it's the time to go back to how things were when the US was founded. We have a vote and top two are President and VP nominees. Keeps the party aligned to what we actually care about and who we think is best, vs who the nominee or party thinks might be best.
No. There's a reason we amended the Constitution not to do that. The system prior to the 1804 election created a deadlock between two candidates that took the House of Representatives (which is responsible for breaking said deadlocks) thirty-six attempts to try to break the tie. https://en.wikipedia.org/wiki/Twelfth_Amendment_to_the_United_States_Constitution
There is no primary. The presidential candidate and the DNC will choose the VP candidate. This is the state of our democracy. Out of 330M people we have been told we can pick from two people, neither of which did we have any part in selecting.