Safe Discharge Voltage for 3.2V 600mAh LiFePO4 Battery and When to Recharge

I want to discharge a Lithium-ion battery which is 3.2V (600 mAh).

1. Will the battery voltage go down if I discharge the battery? I have a battery analyzer (CBA-II) to discharge the battery.
2. In which condition I should charge the batter again? I mean when the voltage will go down to 3V/ 2.5 V/2V/ 0V?

Thanks in advance.

Muhammed I am not an expert on this so I will refer you to batteryuniversity.com which is my go-to site for all information about any kind of battery.    Specifically, they have a page on Li-Ion batteries here.  I do know that LI-ion batteries don't like being overcharged, and also don't like deep discharges.  If you look on the graph on the linked page, they start re-charging when the voltage falls to about 3.6 volts (which is the nominal voltage for Li-Ion batteries.  I'd be wary of letting it go as low as 3 volts - see the links below.
Down the left side of the page you will see links to other articles, specifically I would recommend BU-501a: Discharge Characteristics of Li-ion (just what you're asking)
BU-205 types of Lithium-IonBU-206a: Finding the Optimal Runtime and Power Ratio of Li-ion
Max has a friend who knows more about batteries than I do, so I will try and get him to comment as well.

David,Thanks for the pointer to batteyuniversity.com. I'd forgotten about that site. Lots of very good information there. The only problem is that the first link you put in got messed up. Hopefully I've fixed it. If not we may have to speak to the website folk.

Hi Elizabeth...yes I noticed last night that the link was bad, and the three dots that let you edit had gone... GRRRRR.... was going to post a correction this morning but you beat me to it - thanks.  Except that you spelt it battey.... but the hyperlink works fine! 
Yes Batteryuniversity is a superb site, if you can't find what you want about batteries there, it's not worth knowing.

There is another topical article on this subject here
https://www.eeweb.com/quizzes/lithium-battery-performance-degradation#comment-202430