Hi,
1. There is no option to add an extra fee based on the week day in a custom date field.
We actually plan on having in the future a new option for custom order fields so that you can restrict them to shipping methods.
In that case, you could have two sets of shipping methods with the extra fee added to one of the sets, and then have two custom date picker, each one restricted to a set of shipping methods and then in each one, you could restrict the week days selectable.
2. The information selected in the custom order fields will be visible in the order details page in the backend. There are also settings to display them on the invoice, on the order details page of the customer, on the orders listing of the backend and on the emails. So display-wise, you should have everything you need.
3. Yes, you can also have custom fields for each product. In that case, instead of creating a custom field of the table "order", you could create a custom field of the table "item". These are also only available with the Business edition. In that case, the custom field will appear on the product details page, above the add to cart button, and on the edit popup you get on the cart view in the checkout.