You can go below 3.7v, all the way down to 3v. But your ESC looks at the voltage as a whole. So if one cell goes to 2.9v and the other is at 3.1, you are hurting the lower cell. So it's best to keep a buffer there and stop running above 3.2v. I set mine to 3.4-3.6v.
And yes, you should always charge your battery to 4.2 to run your car. When done, storage charge to 3.7-3.8v
That's a good idea. I usually stop mine before even hitting lvc, and 9 times out of 10 I am right around 3.8v. But I still toss them on the charger for a quick storage and balance.