The maximum or minimum over the entire function is called an "Absolute" or "Global" maximum or minimum. There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.

Is an absolute maximum also a local minimum?

Yes. Yes, not every local max is an absolute max, but every absolute max is a local max (same with min). All an absolute max/min is, is just a local max/min that is greater/lesser than every other local max/min.

Can a relative minimum be an absolute minimum?

It is completely possible for a function to not have a relative maximum and/or a relative minimum. ... As this example has shown there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain.