A female swordtail
Although the hobby has made great advances in understanding the science of what goes on in an aquarium and there have been equally great steps forward in the equipment we use in the hobby, there is still no satisfactory alternative to changing some water periodically.
When in the aquarium the enclosed water undergoes lots of changes over time. dissolved organic matter will gradually build up, the level of carbonates in the water will slowly fall due to the biological filtration processes this means that eventually the pH will also fall. Biologically important minor and trace elements will become depleted as they are used up. Pheromones from the fish will build up and inhibit growth. Nitrates would reach toxic levels
If all these things went uncorrected the aquarium would quite quickly become uninhabitable for livestock and very obviously fail.
But before that happened the existing fish would adapt to the poor condition up to a point and they would appear to be in good health to a casual observer but any new fish entering the system where the nitrates were very high, low pH and lots of dissolved organic matter could easily go in to shock because the changes were to great for its body to adapt to and once in shock the fish could easily die.
The above scenario has and does happen and it often gives rise to a myth where the fish keeper blames the shop for selling poor quality fish which soon die after purchase. Thinking that their own fish look fine so it couldn't possibly be anything they have done!!!
This is less easy to answer because there is no formula for this and there never could be due to the number of variable factors.
The aim of making water changes is to keep the nitrate to an acceptable level, to maintain good growth with the fish, to replenish carbonates and to keep dissolved organic matter to a minimum. It is normally recommended that you change 25% of the water every one or two weeks. In reality this may or may not be enough. The only way to tell is by testing the water for nitrates and KH or carbonate hardness. If the nitrates and KH are being held stable and at an acceptable level then it is enough. However if the nitrates are slowly increasing then more water changes either frequency or volume will be required.
Ideally the nitrates should be as low as possible because nitrate is mildly toxic to fish. You should aim for a level which is below 20mg/l for most fish but there are some delicate fish where even this would be to high.
If your source water has a high level of nitrate to begin with then you will need an alternative.
R/O water is available from most local fish shops or you could install your own r/o unit if you have a lot of tanks. R/O water is almost pure so it will need re-mineralising before use, there are commercial product with full instructions for this. Or alternatively you could use rain water. If rain water is collected and stored properly it is safe to use, native fish have spent their entire lives in it after all.
Yes and no.
It isn't the volume of the water that is changed which may do harm it is the difference in water chemistry which will do the harm. For example if you change 90% of the water on a daily basis then the water in the tank will be very very similar to the supply water which means that there will be no harm in doing this. If on the other hand the water in the aquarium hasn't been changed for several weeks then it will be considerably different to the supply water and making such a large change could prove to be harmful.
No, nitrifying bacteria live on solid surfaces not in the water column so none are removed with water changes. The water going in to the tank however should be close to the tanks temperature and it should be dechlorinated where necessary. R/O water contains no chlorine and so won't need treating.
Don't be complacent about water changes, they are the key to long term success with fishkeeping.