NO, the water is fed through the resin tank at tap/tank pressure gravity.
YES, with frequent use, the resin in the resin tank needs to be replaced and YES, the carbon pre-filter needs to be occasionally replaced, but a TDS meter is supplied with each package to test the water to indicate when these should be replaced.
YES, tap pressure is too high at about 250psi, You will get a tap on the hose to reduce the flow to about 60psi at the head.
NO, you wash with DI water and rinse with DI water. DI (pure) water attracts dirt from the surface (normally, no need for detergent). The rinse is literally.