Do you really think Andy hadn't already replaced at least one 4-minute belt? He replaced it (again), crossed his fingers and sold it to you. If you tilt up a tractor, remove the battery so acid can't leak out. Depending on the model, you may also want to remove some gas (or run it down low) and/or do drain oil (first half of oil change).
Yes. As in the particularly the oil draining to somewhere it shouldn't go...? The gasoline system likely wouldn't have issues. But I don't know about the oil system. 🤷♂️ And I don't know whether the manufacturer says it is or isn't OK to stand the mower in this position.