Are the manners of supplication, such as praising and glorifying Allah and sending blessings upon the Prophet (peace be upon him), and repeating that three times with saying "Ameen," observed in short supplications like the prayer upon leaving the house or entering and exiting the restroom?

Praise be to Allah, and prayers upon the Prophet are encouraged at all times, if a person is in a place where the remembrance of Allah is prescribed. However, one is not required to add anything beyond the supplication mentioned in specific situations. And whoever wishes to supplicate in other than these places, let him observe the manners of supplication and repeat and say "Ameen" as much as he wishes.