The limit is 100k Euro. There is a fund to save deposits under 100k if a bank collapses. The problem is that there is no enough money to save every single depositor under 100k if enough banks are in trouble. That in Italy and everywhere else.
TL;DR: If you have cash in Italian banks, GTFOASAP. If you're a "good guy", buy hard Italian assets (perhaps property), so the money (perhaps) stays in the country, otherwise, get an offshore account (even if declared, and thus perfectly legal, it's much less likely that the Italian government will be successful in grabbing the money, especially if you pick a non-EU jurisdiction, but IANAL).
That makes no sense at all. Just don't keep cash and invest everything except for a small contingency fund.
If you invest instead, you own (a piece of) something physical - a business or a property, typically. A house can burn down and the business can go bankrupt, in which case you lose your investment (unless you're insured). Banks in Italy are incredibly unhealthy at the moment, so to protect your money, you would want to put it in something more healthy, which might simply be a bank account in a not-Italian bank, or as proposed, assets of healthy businesses.
Reneging on an insurance guarantee or forcefully converting deposits to a different currency is a substantially different legal beast than confiscating property (which your shares would be). Perhaps, given that they serve roughly the same end, that shouldn't be the case, but it is.