Not sure of the number of times but there are apps like Battery Bar Pro that show you the percentage of wear on the battery and what its current capacity is VS the original. My SP2 is currently showing 0.4%. Original capacity was 42002mWh and I have 41847mWh.
If the battery dies within the warranty period, the entire unit will probably be replaced. When the battery dies from regular usage, it will be well beyond the warranty period, so it should be many years before that happens; in which case, you'd probably be getting a new computer/tablet anyway.
No. In this case it means a tablet that had nothing physically wrong but had jacked up software or was returned because a customer didn't like it. They wipe the device and reinstall everything and resell it as "remanufactured".