Hello saa, it looks like you are just sort of teetering on understanding the nitrogen cycle. It's complicated and if you don't know about it, you may want to brush it off.
Here's the absolute minimum you need to know to keep fish in good condition:
Ammonia and Nitrites below 0.25
Nitrate below 40
You can do a water change at any time to reduce the amount of ammonia, nitrite, and nitrate in the water. A 50% water change will reduce the toxins by 50%.
If you do a little bit of research, you will find it clear that ammonia and nitrite really DO harm fish. Their gills turn red because they are inflamed (this is something you can see with your naked eyes), which scars them and makes the respiration process much more difficult for the fish's lifetime. Even if your fish survive this process, their longevity is reduced and at some point they will die prematurely.
To expand on the nitrogen cycle:
Ammonia (a highly toxic substance - we use it to kill bacteria and sanitize things in cleaning products like Windex) is one chemical result of fish poop. There are other ways to add ammonia to the tank - this is called fishless cycling. However, since you have fish, this option is out the window so I won't dwell on it too much.
Ammonia is how fish poop first presents itself in our water. Bacteria eventually colonize that eat ammonia, and turn it into nitrite. This is equally toxic. Soon, a second bacterial colony forms that eats nitrite and turns it into nitrate - this is something that can build up as it is only toxic at high levels (like 40-60ppm). We remove the nitrate by doing a water change, and keep our aquarium systems stable.
These bacteria live on your gravel and in your filter. This is why, once your tank is cycled, you don't need to "re-cycle" unless you let your gravel or filter dry out, or do something that kills the bacteria. This includes using water with chlorine in it, or using ich medication, unfortunately.
However, if you keep your bacteria healthy, you will never need to "re-cycle" no matter how much water your change. So with a little patience, you can create a stable, healthy system for your fish.
You are right, fish do introduce ammonia to the water, which is toxic to them. You can just go with distilled water - but you would need to change 50-90% of that water (depending on tank size and fish you have) every day if you don't cycle the tank, and you want the ammonia and nitrite levels to stay safe. If you have an established nitrogen cycle, the maintenance level really goes down
This is because the "cycling" process introduces enough bacteria that they can process the fish poop at the same rate the fish produce it!
I hope this is helpful. I know it all seems confusing and a lot more work than fishkeeping did before you knew about the cycle - but we are speaking from experience and tried & true methods. The fish keeping world has changed a lot in even the past 4 years or so (and changed radically in the last 10 years!), so I'm not surprised your tank-experienced family hasn't heard about it.
In your family's old tanks, the fish probably "hard-cycled" the tank - just got dumped in and slowly adapted to the ammonia and nitrite. They survived, but I wouldn't be surprised if you had die-offs early in the tank, or unexplained deaths down the line. I would chalk this up to ammonia or nitrite related stress, and the permanent effect they have on fish and their immune systems.
The reason some fish survived is that they were able to tough out the bad water conditions until the bacteria could colonize - so even in tanks you didn't purposefully cycle, the process still happened.
So as you can see, the "cycle" will happen whether you want it to or not. It's simply a question of how much stress you want to put your fish though.
Nobody can make you do these things for your fish - it's totally up to you and we aren't going to come yell at you
- we are just advising you how to give your fish the
best care that you can.
All that said, good luck! My advice is not to avoid the research, but to try to quickly get the most important knowledge.