Let’s say I download the data dump of a closed site. The SE site is not available any more and not every one can read the data dump easily. Am I allowed to display the data in readable form on a public site?
It's licensed CC BY SA irrevocably...so yes, you can always make data-dumps public given proper attribution, legally speaking (that's part of their intent). And data-dumps for closed sites should always be available via Area 51 anyway.