Should I be washing my hands before and after meals in independent living faciilty? Can I use dove?

Both. Dove is fine. Any soap can be used. It does not need to be an antibacterial soap. The action of the soap and the friction of good handwashing will dislodge and rinse away 99% of the germs and dirt.
Hand washing. Are you a food services worker? If so, then washing your hands before and after serving food to other individuals is a wise program and typically required. In addition, food service workers are usually required to wear some type of gloving while working with and serving food. Dove hand soap is fine, plus it has moisturizer so that it won't dry your skin with frequent washing.