Short answers: No (yes if you do raw chemistry with temps involved), Yes.
The much longer answer.
Lithium-Ion batteries work on a simple premise. They have a finite recharge life. They base this recharge life on the 80% rule. From the initial charge at the factory till X number of recharges later (between 300 to 500) your battery should be able to maintain 80% or better of that first charge level. This allows the average consumer grade Lithium-Ion battery to last approximately 24 to 30 months. Now remember I answered your first question with a double answer. Constantly doing a complete discharge isn't considered "the safest" method due to temperature issues. IE if you are in certain temp ranges during a recharge you can cause the anode to start oxidizing. Which is what kills a batteries ability to charge. So they actually recommend that you recharge at 40% or higher if possible. The reason for 40%? That is the optimal charge for long term storage of a Lithium-Ion battery.
As far as enough juice to shutdown properly, yes the current iPhones all shutdown with enough power to preserve the on board memory for 12 to 24 hours so you can get it on a charger. That is just a "nice feature" of the iPhone and but isn't needed for proper operation.