```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 not isinstance(count, int) or count <= 0:
                raise ValueError("Copy count must be a positive integer")
            result.extend(original[original_index:original_index + count])
            original_index += count
        elif op == "skip":
            if not isinstance(count, int) or count <= 0:
                raise ValueError("Skip count must be a positive integer")
            original_index += count
        elif op == "insert":
            if not isinstance(count, int) or count <= 0:
                raise ValueError("Insert count must be a positive integer")
            result.extend(count * [original[original_index]])
            original_index += count
        else:
            raise ValueError(f"Unknown op: {op}")

        if original_index >= len(original):
            break

    return ''.join(result)
```