```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 in the chart.")
    if not isinstance(chart[name], list):
        raise ValueError("Reports must be a list.")
    if not all(isinstance(report, str) for report in chart[name]):
        raise ValueError("Reports must be strings.")

    headcount = 1
    for report in chart[name]:
        headcount += team_headcount(chart, report)
    return headcount
```