The filter media is a prime area for bacteria growth, so a portion of the biological filtration may be happening in the filter. The bio filter also 'lives' in the gravel. If you clean both the gravel and the filter at the same time, you may lose a large portion of your bio filter and risk an ammonia spike in the tank. Wait a few days between water changes and filter cleaning to allow the bio filter to bounce back. When you change the water, you will obviously have to replace the lost water with new water.
Tap water contains chlorine which can damage the bio filter.
If you can, place tap water in a bucket the day before you do your water changes. This will allow time for the chlorine to naturally dissipate. You can also buy preparations that will instantly 'age' and dechlorinate the water so you can use it straight from the tap. Another concern with tap water is dissolved oxygen. Place your hand in the water and hold it there.