```python
def draw_stock(shelf: dict, order: list) -> dict:
    """
    Process an order list against a stock shelf, returning the remaining stock.
    
    Validates inputs and order constraints, ensuring no negative stock or invalid
    item references occur. Returns a new dictionary representing the updated shelf.
    """
    if not isinstance(shelf, dict):
        raise ValueError("shelf must be a dictionary")
    
    if not isinstance(order, list):
        raise ValueError("order must be a list")
    
    # Create a copy of the shelf to avoid mutating the original
    remaining = dict(shelf)
    
    for line in order:
        if not isinstance(line, list):
            raise ValueError("each order line must be a list")
        
        if len(line) != 2:
            raise ValueError("each order line must contain exactly two elements: item name and count")
        
        item_name, count = line
        
        # Validate item name is a string (implied by "item name")
        if not isinstance(item_name, str):
            raise ValueError("item name must be a string")
        
        # Validate count is a non-negative whole number (integer >= 0)
        # Note: The prompt says "positive whole number" for order lines, 
        # but also says "Reject a shelf count that is not a non-negative whole number".
        # Let's re-read carefully: "Reject ... a line whose count is not a positive whole number".
        # So order line count must be > 0.
        if not isinstance(count, int) or isinstance(count, bool):
            raise ValueError("order line count must be an integer")
        
        if count <= 0:
            raise ValueError("order line count must be a positive whole number")
        
        # Check if item exists on shelf
        if item_name not in remaining:
            raise ValueError(f"item '{item_name}' not found on shelf")
        
        # Check if enough stock is available
        if remaining[item_name] < count:
            raise ValueError(f"insufficient stock for item '{item_name}'")
        
        # Deduct stock
        remaining[item_name] -= count
        
        # Ensure zero-count items remain in the mapping as per requirements
        # "every shelf item still present even when its count reaches zero"
        # Since we initialized from shelf and only subtract, if it was there, it stays.
        # If it reaches 0, it stays as 0.
        
    return remaining
```