You can certainly bring a small backpack into the parks with any of the items you mentioned. You are allowed to bring water bottles, books, snacks, and general personal and child care items anywhere at WDW.
You should, however, be aware that there is a security screening area at the entrance to each of the theme parks. Just before the park entrance, you will see rows of tables manned by security staff. They will ask you to open any purses, backpacks, diaper bags, or other similar containers and they will look inside. There are simply looking for any potentially dangerous items. (I wouldn't, for example, try to bring a large pair of scissors into the parks.) If you have items that you would feel comfortable having in your purse at your local mall, for example, then chances are it will be fine at WDW. There are plenty of security tables and the lines move fairly quickly.
Have a great trip.