During cycling, water changes need to be as big as necessary to get the level down to zero. As long as the new water is roughly the same temperature as the tank water the fish will be fine. Testing with your hand is close enough.
Once the tank is cycled, weekly water changes of at least 50% should be done. Ammonia and nitrite will always be zero in a cycled tank; nitrate may increase if there are no live plants. But water changes do more then remove nitrate. They also remove many other chemicals exctreted and secreted by the fish which we can't test for, and they replenish minerals taken up by fish, plants etc.