Yes the Kinesiology tape is water resistant. You can shower with the tape in place. Later you can air dry the tapr or wipe with a dry towel. Do not use a dryer on the KT tape.
It is recommended not to wear a kinesiology tape for more than 5 days. The length of time it stays depends on where the tape is applied. When the tape is applied to a knee or foot which is naturally a harsh environment for tape, it will generally last on for 2-3 days.