Diablo – Does Big Bad Voodoo stack

They do not stack as you will only ever see one buff of that type on the target.

Drew data from this question and links. Do damage over time effects stack?

Since it is a debuff on the target you will only see one Marked for Death on the target, a new cast or other cast will simply reset the timer. If there is similiar type buff then it would be a different debuff on the target and should stack.

Edit: To answer the additional edited question, if we refer to this question then one can assume that they do stack because of the different runes. However, this is a debuff casted on a target, not a buff for the party. So I believe the answer is still they will not stack, but whoever cast the most recent one will have that effect. I don't know another demon hunter to test with at the moment, but I will update once I do.

Mantras do not stack in a literal sense. Meaning two of the same Mantra won't provide double the results. However, two+ monks with two+ different Mantras active will stack as long as they are completley different Mantras. Alternativley, two+ monks with two+ of the same Mantra with different runes will stack. You can still gain the rune benefits from a Mantra, but you will not be doubling its effect.

You can see a conversation about it here and here.