My adds to your summary:
-biopellets are made of a solid carbon polymer
-bacteria stick to the pellets and use it as a carbon source (our tanks are usually carbon limited)
-they consume a lot of nitrates, and a much smaller proportion of phosphates, plus the carbon from the biopellets to grow
-as they tumble in the reactor, they are sloughed off the pellets and washed out the effluent of the reactor
-ideally the effluent is plumbed directly to the skimmer so no bacteria makes it into the system or but some people also just put the effluent in the skimmer chamber of the sump and have had good results
-you just top off the media... I do it roughly every 6 months. One package of biopellets usually lasts me like 3 years!
Understand that it's heavily skewed to remove nitrates and that you'll still probably end up needing to run GFO with it... despite some manufactures claims that it'll keep your phosphates as low as you want it too, IME.
Also, as it is ramping up with bacteria in the first 4 weeks of operation, don't be surprised if your corals look really ticked off. They are adjusting to the nutrient level drop. All my SPS looked ticked and some almost always STNed in the initial but as long as you're diligent and superglue any parts that are STNing and assist them in making it through the initial adjustment period to biopellets, you shouldn't have a problem after that.
Also, keep your alk typically lower, around 8 dKh or lower. If you get above that, you tend to have issues with SPS.
My old 125-gallon ran off biopellets, GFO, and an oversized skimmer. If I had any input to your system... I think you may need to start looking for a more robust skimmer if you plan to implement biopellets. Your skimmer will get the job done but a higher rated one will do a better job.
Hope it helps!