```python
def apply_overrides(base: dict, overrides: list) -> dict:
    if not isinstance(overrides, list):
        raise ValueError("Overrides must be a list.")
    
    merged = dict(base)
    
    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:
            raise ValueError("Each override must contain exactly one equals sign.")
        
        name, value = parts
        
        if not name:
            raise ValueError("Setting name cannot be empty.")
        
        if name not in base:
            raise ValueError(f"Setting '{name}' does not exist in base.")
        
        merged[name] = value
    
    return merged
```