Hi Hazel,
Thanks for visiting the Disney Parks Moms Panel with you question!
The answer to both parts of your question is yes - the food court at your resort will accept your Disney Dining plan; however, you will need to use a quick service credit to get a meal there. You could also use a snack credit if you are only looking for a bite to eat.
When you arrive at your resort, your Key to the World Card will have all of your dining entitlements that come with your Dining Plan loaded onto it. When you dine, you will give the server (at a table-service restaurant) or the cashier (at a quick-service restaurant) the card. They will deduct the appropriate entitlement from your Key to the World Card. There is some really good information on this at the
website on Disney Dining Plans, including links to download brochures with which restaurants are covered under each plan.
I hope that this information helps, Hazel. Please do not hesitate to ask if you have any further questions - we love helping you to plan your Walt Disney World vacation!