The foam is just insulation to keep the fuel cold before lift-off.
A new design for the insulation factor is needed since it is clear that this flimsy-any-kind-of-other-foam-as-well design is too dangerous to the shuttle now (same problem was there for the first 100 flights though.)
Solid rocket booster instead, thicker tank, up-to-the-minute fueling, new vehicle are the only options really.
Will be a long time and lots of testing before she goes up again.
I don't think so. We didn't have the problem until the enviros made NASA get rid of the original insulation - which never failed. Since the change, there have been failures on every mission.
You could look it up.
http://capmag.com/article.asp?ID=2942