If your tank is cycled and you are doing 25% water changes every week, you aren't neglecting your fish! I personally test before every water change, as it just gives you the peace of mind that everything in the tank is going well, parameters are still stable and nothing has caused a mini cycle. Once a month is fine as long as the parameters are still good (0 ammonia, 0 nitrite and ideally <20 nitrate), you don't really need to test more often. It's really personal preference unless there seems to be something wrong with your tank/fish.
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Once the tank is cycled and seasoned (running for about 3 or 4 months) you only have to check the nitrates weekly. As you get comfortable with your tank, and if you don't change anything, you only have to check the nitrates monthly. Once you make a change, such as adding stock or plants, check ammonia, nitrites and nitrates again for a week or two and if it is still holding steady, go back to checking nitrates monthly.
I check my parameters weekly with my water change. Its just a good routine for me. So I know im doing everything I can.
I even have a dry erase board next to my tank with their feeding schedule and different fishy equipment I will obtain in the future
A mini cycle is caused by one of two things. Adding bio load, or changing/removing something that holds a beneficial bacteria colony.
Your tank only produces enough bacteria to consume the ammonia produced in the tank. Any more bacteria would starve.
If you add more ammonia production (bioload = any living creature that produces waste), it takes a little while for the bacteria to multiply enough to handle the new level. If it's a small increase (1 small fish/shrimp), you may never even notice the mini-cycle. If you add a large bioload (10 fish) you risk a potentially dangerous ammonia spike, because the bacteria will take longer to adjust. Beneficial bacteria duplicate every 13-24 hours depending on ammonia level and tank temperature (warmer=faster)
If you remove a surface that contains your bacteria, the remaining bacteria has to duplicate somewhere else to cover the ammonia that colony that you removed was handling. Bacteria grows on every solid surface. Most lives in the filter where the most oxygen flows through, but they also live on other surfaces. If you changed your substrate, or removed several ornaments/one large ornament you can kick off a mini cycle.
As far as ammonia, nitrite, nitrate; basically never, only if something seems really off. Be it fish are acting up, or the tank smells different. Yes, you read that right I go by smell, a healthy FW aquarium smells earthy/mossy. Anything different could indicate a problem.
I will check hardness and pH a couple of times a year. And I check the tap water a few times a year.
Now, here's the caveat - my tank is well established (been up for 5+ yrs), and the stock isn't changing. If I was to start a new tank, I would test regularly (once a week) until I had confidence that it was stable, and then I'd go back to using my experience.
If I was to add stock to my existing tank, I might check ammonia a couple of times for the first week to ensure I don't get a mini-cycle.