Regarding the center on current position button, I would even go a step further:

In menu there are also options to center position automatically and to rotate mapview automatically. I would remove these options from menu as well. The option for rotating the mapview is already on the map view and is there the better choice.

Further on, I think people expect, that the center button in map view works similar than the rotation button, but it doesn't. That's in principle OK, because there is a further option and therefore the option in the menu is a different one as that on the mapview. Anyway for me it would be better when I could also switch to the automatic enter position mode from mapview. So I would suggest the following:

Remove both options from menu. Add an indicator on the buttons in mapview, that the options are active. Functionality of the rotation button can stay as it always was. Functionality of the center map button gets a further option: If you want to center once just make a short tap on the button. If you want it to center automatically make a long tap on it.

I hope I described my proposal in an understandable way.