No. Well, yes and no. Most daycares will feed your baby the milk (breastmilk or formula) that you prefer for your baby to consume. As the child gets older, meals such as breakfast, lunch and snacks may be provided by the daycare. Diapers are often items that parents provide specifically for their own children as individual babies may respond differently to different diaper types and brands.
Yes. Most day cares do provide diapers and many provide food for toddlers (usually at an extra price). Every day care is different, so it's best to have this as one of the questions that you ask when investigating which day care facility to choose.