A monarchy can be like a dictatorship or it can be part of a democracy.

True

A dictatorship can also be a democracy.

False - You can't have a democracy if citizens have no control, which they do not in a dictatorship.

A democracy can have both representative and direct characteristics at the same time.

True

A government can be both a monarchy and an anarchy at the same time.

False - A monarchy has someone in control. Nobody is in control with anarchy.

Theocracy can co-exist with monarchy.

True

Theocracy can co-exist with democracy.

True