Regarding your edit, no, you don’t need a majority of Senators and no party has in a couple decades. What you need to form government is a majority in the House. However, at times when a majority has nog been possible, a PM can be decided when they have a majority of MPs in the House that will vote with them on confidence and supply. Confidence is a literal vote of confidence that happens, where if it fails, the PM is ousted and an election happens. Supply being the budget, which, if it can’t be passed, also triggers an election. Hence why Australia could never have a US-style government shutdown.
Regarding your edit, no, you don’t need a majority of Senators and no party has in a couple decades. What you need to form government is a majority in the House. However, at times when a majority has nog been possible, a PM can be decided when they have a majority of MPs in the House that will vote with them on confidence and supply. Confidence is a literal vote of confidence that happens, where if it fails, the PM is ousted and an election happens. Supply being the budget, which, if it can’t be passed, also triggers an election. Hence why Australia could never have a US-style government shutdown.