The hijackers were Saudi nationals, but the operation was in no way sponsored by the Saudi state, which is a staunch US ally. Which is why the US proceeded to (attempt to) flatten Afghanistan instead.
We do not know this. There are plentiful evidence to suggest direct involvement of the state itself, and the bin Ladin family is certainly hard to untangle from the Saudi state. That is just from what we can know from unclassified sources.
It seems to have made things better for the Taliban.