Empty set in a simplicial complex Should the empty set be considered a simplex in a simplicial complex?
Which justifications exist for the answer?

I guess it is somewhat comparable to $1$ not being a prime number.
This is a useful construction in homotopy theory and is probably easiest explained as the augmented simplex category.
I think your answer is yes.  If the intersection of two simplices in a simplicial complex is a face (sub-simplex) of each, then an empty set must be a simplex.