Are you allowed to play a monster in face up defense position?

Question

My understanding is that as far as normal summoning goes, you can either play a monster face up in attack position, or face down in defense position. You cannot mix them, e.g. face up defense position or face down attack position. Is that correct?

Answer 1

Is that correct?

Yes.

When you normal summon or set you can only do it in face up attack position, or face down defense position, respectively.

There is no thing as "face down attack position". There was before, on the Darkness Approaches card, but it had an errata that removed that effect.

You could however special summon a monster on face up defense position if it is possible. One example may be any Synchro, XYZ, or Fusion Summon you carry out, where you can select how to place that card (unless otherwise restricted).