```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("overrides must be strings")
        if '=' not in override:
            raise ValueError("override must have an equals sign")
        name, value = override.split('=', 1)
        if not name:
            raise ValueError("override name must not be empty")
        if name not in merged:
            merged[name] = value
    return merged
```