```python
def validate_node(node):
    if isinstance(node, dict):
        for k, v in node.items():
            if k == "children":
                assert isinstance(v, list), "Children must be a list."
            elif k == "bytes":
                assert isinstance(v, int) and v >= 0, "Bytes must be a non-negative integer."
            else:
                return False
        return True
    else:
        return False

def file_paths(root: dict) -> list:
    if not validate_node(root):
        raise ValueError("Invalid root node.")
    
    def walk(node, path):
        if "children" in node:
            for i, child in enumerate(node["children"]):
                walk(child, path + [str(i)])
        elif "bytes" in node:
            return path
        else:
            return []
    
    return list(filter(lambda x: x, map(lambda p: "/".join(p), file_paths(root))))

def tree_bytes(root: dict) -> int:
    if not validate_node(root):
        raise ValueError("Invalid root node.")
    
    def walk(node):
        if "children" in node:
            return sum(walk(child) for child in node["children"])
        elif "bytes" in node:
            return node["bytes"]
        else:
            return 0
    
    return walk(root)

def heavy_folders(root: dict, min_bytes: int) -> list:
    if not isinstance(min_bytes, int) or min_bytes < 0:
        raise ValueError("min_bytes must be a non-negative integer.")
    
    file_paths_list = file_paths(root)
    total_bytes = tree_bytes(root)
    
    return list(filter(lambda x: walk(root, *x.split('/')) >= min_bytes, file_paths_list))
```

This solution includes the `validate_node` function to ensure that each node in the tree is valid. The `file_paths` and `tree_bytes` functions are implemented using recursive walks through the tree. Finally, the `heavy_folders` function filters these paths based on the total bytes of the folder, applying the minimum byte requirement.