```python
def team_headcount(chart: dict, name: str) -> int:
    if not isinstance(chart, dict):
        raise ValueError("Chart must be a mapping.")
    if name not in chart:
        raise ValueError("Name must be a key of the chart.")
    if not isinstance(chart[name], list):
        raise ValueError("Reports must be a list.")
    for report in chart[name]:
        if not isinstance(report, str):
            raise ValueError("Report must be a string.")
    
    count = 1
    for report in chart[name]:
        count += team_headcount(chart, report)
    
    return count
```