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I have a route with an origin, a destination, and 0 or more waypoints. Will Google calculate the route in the same way every time? If for example, I will save the coordinates of all the points in the database, and I want to redraw it later, is it guaranteed that the map will look the same as when the points were first created?
No.
Maps change over time as new roads are built, and Google is constantly updating their mapping data to match.
Also, Google permits users to edit routes and suggest corrections to driving directions, which they take into account for future calculations.
Also, Google makes changes and improvements to their mapping algorithms from time to time, and they are not guaranteed to stick to the same algorithm in the future.