Yes and no. 0% you should be fine, but generally speaking you'll get longer life out of LifePO4 if you stay between 10% and 80%. Most battery based PV systems are installed to shut off (or switch to grid) at the 10% SOC mark for this reason.

Yes, thousands of times, an order of magnitude improvement over lead acid. And the increased capacity means that they're much less likely to hit 0% (or whatever defined cut-off you set) during a typical outage anyway.