I was in an environmental program at school where we tested a large variety of local water sources. Test kits were a bit different when testing actual streams and such - we measured total dissolved solids, dissolved oxygen, phosphorus, nitrates, temperature, pH, and more I can't remember off the top of my head. We would collect macro-invertebrates and fish as well to see what was living there.
As far as the usefulness of the master test kits API has for actual streams and bodies of water:
You aren't likely to find any Ammonia or Nitrites in streams at all, so there's not much point in using those. Nitrates are an either or situation - in the vast majority of cases you'll see no Nitrates at all. Or you'll see crazy high nitrates if you are in an unhealthy water source that might be getting eutrophic. pH and temperature change so much by time of day, season, and weather that I haven't found them very useful. I always took them and wrote them down, but they're mostly meaningful when comparing results from the same time, season, and location in years past to look for patterns. Or if you're checking the variations in pH from the same spot at each month of year, so you can see the range. Even just a tree's shade can lower the water temperature a good 15 degrees, and seasonal variations and rainfall can change up the pH more than you'd think. There's a reason fish care sheets usually give pH and temperature in ranges, even for wild caught fish.
If you're really interested in your local streams and waterways and you get only one test, I highly recommend dissolved oxygen. You do have to make sure not to get your sample at the very surface or right against the substrate, as that will affect the results. And make sure you aren't by riffles, rapids, or still pools to get a good idea. But of all the tests I did, high dissolved oxygen meant the water would have the highest amount of varied life. Low dissolved oxygen was often paired with other pollutants. You can even predict what bodies of water will be worth collecting some of the more attractive fish and rarer invertebrates by collecting in areas with the highest dissolved oxygen levels. Assuming you have all the legalities covered for being able to collect natives.
Total Dissolved Solids is my second favorite test. Eventually you'll start seeing a pattern in TDS and what the specific conditions of that stream are - how clear the water is, if it's over silt or rock, what type of vegetation is around, etc. You'll likely start to see patterns in the types of critters that call certain areas home based on TDS, too. It gives you a better idea of what type of specific habitat that section of creek/stream/pool is.
For pollution levels, phosphorus is the best test. If there's a ton of phosphorus, it will test high on other pollutants, and things like dissolved oxygen will also be poor. If the phosphorus is really high practically nothing will live there except huge numbers of leeches, and it's usually safe to say that there's some pollution being caused by people like a nearby construction site.