It can regenerate its ears, cartillage[2], cardiac muscle after cold-induced lesions[3] but sadly not after infarction/reperfusion[4] and digits (to some extent, in neonate mice)[5]. There may be more.
[1] http://www.pnas.org/content/107/13/5845.full
[2]http://www.eurekalert.org/pub_releases/2001-08/wi-rit080201....
[3] http://www.pnas.org/content/98/17/9830.full
[4] http://onlinelibrary.wiley.com/doi/10.1111/j.1067-1927.2005....
[5] http://onlinelibrary.wiley.com/doi/10.1111/j.1524-475X.2007....
I find it reassuring that this unknown thing was right on our doorstep, and it makes me wonder what other amazing discoveries are just out of reach (or even within reach...) The world is more complex than we see; all we need do is look (a lot...) - There is more in heaven and earth than is dreamt of in your philosophy, Horatio - Nature's imagination is greater than your imagination
From the article, it seem to not be so much that it enables healing, but that it enables healing without scars. I expect this is crucial in some situations, but it's not clear that it can heal what wouldn't otherwise heal. Certainly, there are cosmetic applications.
Most probably, but not necessarily.
A gene can be present without being useful because it is linked to another gene that is itself useful; or it can be a leftover from an earlier moment of evolution where it was useful, and then it ceased to be useful but there was never an evolution pressure strong enough to have it disappear.
In summary, just because a gene is present and active does not mean it's useful today.