1 - Yes, your understanding is correct. 2 - The minimum voltage required to charge a 3.7v Li-Ion battery (to 3.7v), is 3.7v. A more practical voltage would be, 4.0v (3.7 < 4.0 < 4.2). A more "realistic" example of the second part of the first sentence would be 10 hours at 100mA.
