Can I apply for a visa in Hanoi after arriving in Ho Chi Minh City, and what happens if my application is rejected?

maybe if you fly same day as arrival, they could see it as a connecting flight. Make sure to add your boarding pass for both flights, hotel booking in Hanoi to the application. But the biggest issue is that starting Saturday the whole country shuts down for a week for Tet (lunar New Year) so if you apply today, you won't be approved until 5 or 6 February at the earliest