If there are ways to violate causality they are likely restrictive enough that we can't use them to violate causality prior to when we knew about the methods (roughly). This is true for most proposed causality violating mechanisms. For example, you might be able to violate causality with a wormhole, but you can't do it to any point in spacetime prior to the existence of the wormhole.
In general, if there are causality violating mechanisms we should expect that they can't violate causality so severely as to make the past become radically altered since we just don't see that. It is conceivable that such manipulation is possible but that once we find an effective method of violating causality we will be quickly wiped out (possibly by bad things related to the method itself) but this seems unlikely even assuming one already has a causality violating mechanism.
Mostly agree. Would downgrade to "can't or won't". Apart from a little more completeness the difference makes a difference to anthropic considerations.
http://www.nature.com/news/2011/110922/full/news.2011.554.html
http://arxiv.org/abs/1109.4897v1
http://usersguidetotheuniverse.com/?p=2169
http://news.ycombinator.com/item?id=3027056
Perhaps the end of the era of the light cone and beginning of the era of the neutrino cone? I'd be curious to see your probability estimates for whether this theory pans out. Or other crackpot hypotheses to explain the results.