Can I Display the Winning Recipes and Photos on My Site?

Yes, as long as entrants agreed to it. The clean way is to ask for that permission in your terms and have each entrant accept them when they enter.

1. On the Setup tab, click Modify on your Terms & Conditions and add a line under Additional Terms saying you may publish entries, names and photos on your website and social channels.
2. Add a Terms & Conditions checkbox from Add Field on the Pre-Entry tab, so every entrant agrees before entering. Custom fields are on the Business Plan and above.
3. Collect recipes and photos with the Upload action (Business Plan and above), then show the winners in a Gallery on your site.

Only credit an entrant by name if your terms say you will. And if a recipe came from a cookbook or someone else's site, the entrant may not own it, so ask for their own recipes in the instructions.