For any governmental experts out there...if on a given day, Democrats outnumber Republicans in the House, one requests removal of the speaker, and a vote is taken, could the speaker then be a Democrat, until the next time there's a Republican majority?

Is this a method for the House passing legislation that's then sent to the Senate and signed by the president same day?

We know that only budget-related bills require a simple majority in the Senate. Asking for a friend...