If all of the FS characters are dead, odds are many of the non-FS characters will be as well, in which case there will be a whole lot of other things to worry about. If that ever comes to pass it will be dealt with then; there's no sense in speculating on unlikely possibilities in the meantime.
The admins do not have playing characters. At the very beginning, naturally the original force sensitives needed to be informed of their force sensitivity in order for there to be players capable of testing others for FS. That has no further bearing on the present, though; the Combine is designed to be interactive, and therefore you do need to seek out someone capable of testing you if you desire to be tested. Most people do this through their faction's connections eventually.
So, if I read the rules correctly, if you get tested and are found NOT force sensitive, all is not lost. You can test again after you have leveled up and have a better chance of becoming FS. Is this correct? Also, is there a limit on how many times you can be tested? I guess why I ask is, can you test multiple times, say at level 2, and become FS, on attempt #10?
Every 5 levels the server rechecks your Force Sensitivity and stores the new value (whether FS or not) in the database. When you are tested, the server checks the database, and returns a result based upon that value. Being tested multiple times at the same level does not alter your chances of being FS at that level.
"May the Grace of Ara go with you, and His Vengeance be wrought upon your enemies."
So if it rechecks it every five levels, well lets say I'm FS now and I get to level five without being tested then will it re-roll and possibly roll that I'm not FS or does it just do that if you're not FS?
No. The skill to test other beings for their force-sensitivity is a skill, and just like any other force power, needs to be learned first. However, not every force-sensitive person automatically learns how to test others, as that skill is merely one choice of many.