Are these tzitzis kosher? Are tzitzis with zippers kosher?
Looks fine to me. The main thing is when you unsnap it, it has to be for than 50% open.
This shirt was meant to be worn alone (ie nothing over it). Can it be worn completely closed or would that make it pasul?
It can be closed. It just needs to be possible to unsnap it and be 51% open. I assume if it was made for this it was done right.