1. 一週間しか上映されない 2.一週間だけしか上映されない I think 1 is better grammatically, but the speaker of 2 wanted to emphasize how short the term is.

This sentence gives emphasis like "just only". It means the same as: この映画は一週間だけ上映される。 この映画は一週間しか上映されない。 I hope this was helpful.

The nuance of the expression has already answered. so... to me, it seems like that example sentence is more like written expression than colloquial expression. in my opinion, we don't really use ～だけしか when we actually speak to people. I often see such expressions in articles on papers or on the internet.

I think, だけ≒only しか≒few only few≒There are only a few this movie, so Will be shown that among one week.