He needs to establish himself as a leader (this behavior doesn't help beyond maybe their base) if he wants to be president after Trump. It's also ingratiating behavior towards Trump which will help ensure he remains on his good side and part of the in-crowd.
I think it's actually Thiel who is in control and pulling the strings here. He essentially got Vance into his current position and is obviously still linked to Musk.
Maybe. Trump's temper can still get him sidelined. He needs to remain front and center to be a viable candidate in 2028. And nothing about Thiel or Musk suggest they'd throw money at him out of loyalty, they'd throw money at him if they thought he could win. Otherwise, they'd find another candidate.