How do I see if a node exist in a binary tree, and if not print a message saying it does not exist

Trees can be traversed in many ways, mostly used are: Inorder, Preorder and Postorder.

Following breakdown of steps would help:
1. Use one of the tree traversal methods and check if the current node matches with the node you are searching for.
2. If found, delete the node and stop traversing further
3. If the tree is completely traversed and none of the node matched then display Node not found.

// Using preorder traversal
bool checkIfNodeExists(struct Node* node, int key)
{
    // empty node/nothing to search in
    if (node == NULL)
        return false;
    
    // node found
    if (node->data == key)
        return true;
 
    // recurrsion on left subtree 
    bool resultLeft = checkIfNodeExists(node->left, key);
    if(resultLeft) 
      return true;
 
    // recurrsion on right subtree
    bool resultRight = checkIfNodeExists(node->right, key);
    if(resultRight) 
      return true;

    // node not found
    return false;
}

Quote:

void delete_tree(binarytree *tree, int val)

Your method looks way too complicated. You should extract the common logics out of it.

This method should pass the node you are searching to delete to the checkIfNodeExists method and based on the result, take an action of deleting or messaging (if not found). This would make it easier for you to see where you might be missing something and need to make change.