0 nitrates is good to have, but near impossible with a cycled freshwater tank. Fish waste turns into ammonia, bacteria turn ammonia into nitrite, different bacteria turn nitrite into nitrate. Usually it stops right there in a freshwater setup. Plants will grab some of the nitrates, but usually not enough to keep them at 0. Water changes is the way to get rid of the nitrates (basically by diluting them to low enough and safe levels), but even with plants you have to take the nitrates back out (by pruning the plants so they don't grow out of control). Chemical filtration is also possible - there you get rid of them by replacing the chemicals.
Water changes will not hurt the cycle any if all you do is change the water. If you disrupt or clean the biological media of your filter, then yes you would slow the cycle down or if overdone kill the cycling. Depends on your filtration where the bacteria live (to be effective they have to attach to surfaces, so freefloating in water won't help). Sponge filter, they live in the sponge - rinsing out the sponge to clean will take some bacteria with it. Under gravel filter - bacteria live on gravel - vacuum gravel will take out some bacteria with it. And so on and so on.