Can you somehow do something about it that players can only eat and degrade on a Minecraft server?

There's an area on my Minecraft server where carrots, potatoes and the remaining seeds apart from pumpkin and melon can be planted. All are in adventure mode. Players can only plant and harvest seeds, carrots and potatoes. How is that possible?

You have to load a plugin onto the server. Just enter bukkit on the Internet on the page you will find some. You can then protect certain things with it, for example. If you don't know how to install a plugin, just watch a tourorial on YT