So my questions. When I go to the archery range, every other bow I see guys shoot have a stabilizer. Am I losing anything by not having one?
More weight further away from the pivot slows down form torque. So usually if you have a stabilizer you have fewer L/R flyers and the ones you do have are usually less severe. Also, to a lesser degree, it slows down torque from heal pressure reducing high flyers too.
No issues yet but should I just automatically replace the string every so often?
Every couple years a string should be replaced. Since they are made of plastic strands they do have a limited shelf life. If you shoot very little and keep it in a closet where no light hits the string you can go longer. But usually it's good to observe the two year rule...or sooner if it shows excess wear.
Also it seems a little loud to me when I shoot it. Can anyone recommend a good string "silencer"?
String and cable silencers are not a bad idea on that bow. Myself, once I tried Sims stuff I never went back to anything else. String Leach, Cable Leach and Limb Saver/dampeners would all be on my bow if I shot the Pantera.
Lastly, how long will a compound bow last before you start losing strength in it?
That bow should not lose any strength/poundage. It should remain the same until the day it breaks. With a club and hinge limb breakage could be tomorrow it could be 15 years from now. You just never know with that design.