I don't know the history of your tank and/or how well it may be cycled. Prior to filtering, you were adding a fair amount of ammonia and nitrates with every water change. I don't know if your BB colony(ies) were up to the task of handling it before stock were negatively affected.
It is not clear if your problem is disease from the fish you received, or if the ammonia level went very high from adding so many fish at once. (Note that some species are much more sensitive to even low levels of ammonia than others.).
As for the Prime and ferts, you would add ferts a day or two following the water change. Prime 'detoxifies' metals through bonding that makes them less or unavailable to plants.
As to dosing Prime for the entire tank, it's a preference and safeguard and can yield benefits, especially if/when water with negatives is being added directly to the tank at a reasonably fast rate. If you add directly to the tank and only add an amount enough for the water being added, you have diluted the product below it's recommended dose. The only way to truly add conditioner for the exact amount of water being added, would be to do it outside the aquarium in buckets or bins.
Finally, I still think your pre-filtering method misses the opportunity to also remove nitrates. I highly recommend API Nitra-Zorb.
Having said (er written) all of this, the pre-filtering/water staging process does allow for more stable water since O2/CO2 and pH stabilize. You're on a well and likely don't have chlorine, but if you did, the process would allow it to dissipate also.
So how well established is this tank? Are you confident that the BB colony(ies) is/are sufficient to handle the stock level...Also, with the level of ammonia and nitrate in your well water, I wonder/worry that your tank nitrate levels may be very high.