Yes filters should be clean and if you leave the feces in there it will show in your nitrate test. Use dechlorinated water to rinse the media so you don't kill the bacteria.
You can use baking soda instead of salt but not in the same proportions.
Because you don't want to change pH or GH or KH that is in your tank right now (because you have been using salt) by more than the smallest amount, you have to match new water you add to the parameters of the water that is in your tank now.
By adding aquarium salt you are already messing with pH, GH and KH. You may be able to transition to pH=7.6 but it has to be a gradual transition over a period of weeks or months.
Know that if you change your KH or GH it will impact your pH...they are interrelated.
Do not use NaCl at all. Baking soda usually does the trick, but you have to know your test results from tank and tap before you decide.