The Nitrate test is the least reliable of all the mast test kit, mainly due to the fact that the bottles of reagent solution has to be REALLY shaken well, I do mean shaken well as the power form of the solution inside the solution sticks to the inside walls of the bottle, a couple of members state that a bang or two of the bottle on a table will help loosen these up. THEN you may get a more accurate test of nitrate.
But having said all that, I never really worry about nitrate, especially if you have a fair few plants and do at least a 50% once weekly water change.
Api stress coat, stress zyme all do not a lot for your tank. Just try to keep as much chemicals away from your tanks as possible, I only ever use dechlorinator for the water changes, thats it.
Quick Start is actually something that helps to kick start the process of cycling your tank, I am assuming here that your tank is cycled and has been runing for a while, but you have not yet fully cycled your tank then this could be a factor.
Overfeeding can have a effect on ammonia levels, but its not good fishkeeping practice to overfeed anyway, this can cause many issues, including poor water conditions.
Overstocking certainly is an issue, perhaps if you can give a list of what you have in your tank and how many, along with tank dimensions and what water you have, soft or hard along with a pH reading. We can hep determine if this is a factor in your ammonia readings, but also helps to avoid potential issues with compatibility and aggression issues etc.
Cleaning the filter should only be done when you have to, ie the water flow from your spraybar or nozzle is noticably reduced then thats when you need to give the impeller a clean along with a light clean of the filter casing, do NOT overclean this as this is where a good number of you bacteria lives. As for filter media, just was half of the sponge you have in old tank water, just squeeze them to get rid of the worst and put them back into the filter. that should do it.
But all in all, having a cycled tanka nd filter should mean you get ZERO readings for ammonia and nitrite, the two most toxic forms for your tank stocking, if you are still having readings of 0.25ppm ammonia, then one or a combination of the above may be a factor. Don't forget false readings of ammonia is a factor as well.
And of course, human error in doing these test could be something to consider. When i first started the hobby, like you, i got strange readings sometimes and insisted i did the tests right etc etc, until i went step by step with another member and the one thing i did not fully do between each testing was to ensure the test tube vials was fully cleaned out, residue from previous tests could affect you test readings. Certainly something i surely learned and never forgot.