The topic is the question. How do I save? Are there savepoints or how else? I can't find the function.

Yes they are save points, they look like large gold coins on the ground with a P in the center also in the options menu there is a option to enable Auto-save which will save the game at every screen transition such as entering or exiting a building, ect. keep in mind this can lead to some undesirable situations such as having your party near death after getting done with a major battle and having no healing items only to leave(and the game autosaves) and end up having the game drop you off where another major battle is about to happen.