```python
def apply_edit_script(original: str, script: list) -> str:
    if not isinstance(original, str):
        raise ValueError("original must be a string")
    
    result = ""
    original_index = 0
    
    for op, count in script:
        if op == "copy":
            if count <= 0:
                raise ValueError("copy count must be a positive integer")
            result += original[original_index:original_index + count]
            original_index += count
        elif op == "skip":
            if count <= 0:
                raise ValueError("skip count must be a positive integer")
            original_index += count
        elif op == "insert":
            if not isinstance(count, str) or not count:
                raise ValueError("insert text must be a non-empty string")
            result += count
        else:
            raise ValueError(f"unknown op: {op}")
    
    if original_index != len(original):
        raise ValueError("script stops before the original is used up")
    
    return result
```