```python
def apply_overrides(base: dict, overrides: list) -> dict:
    if not isinstance(overrides, list):
        raise ValueError("Overrides must be a list.")
    
    result = base.copy()
    for override in overrides:
        if not isinstance(override, str):
            raise ValueError("Each override must be a string.")
        
        parts = override.split('=', 1)
        if len(parts) != 2 or not parts[0]:
            raise ValueError(f"Invalid override format: {override}")
        
        name, value = parts
        if name not in result:
            raise ValueError(f"Override name '{name}' is not in the base settings.")
        
        result[name] = value
    
    return result
```