Hi @awstudio,
Is it possible to manually create invoices for orders outside of my webshop, for example at fairs.
Yes, you can create manually invoices, but I think your actual question is whether you can create a manual order and then create a manual order for it, right? If so, the answer for both questions is: Yes, you can!
Also, if you need to set manually products, that is, products that aren’t in your inventory/database and/or you won’t want to save there, but only use it in manual orders, this plugin may be helpful for you: WooCommerce Quick Manual Products
Also it is possible to modify the invoice numbers?
Yes, you can edit the invoice number within the PDF document data panel, under the order details page:

Please note that this is a per-order basis setting, and it doesn’t affect the Next order number setting, under WooCommerce?> PDF?Invoices?> Documents?> Invoice, which is a global setting used to generate the invoice number automatically when the PDF document is attached in an order email notification (that you can configure under the Attach to setting, located under this page too).
Therefore, after editing invoice numbers manually, make sure that you have set there the actual next invoice number, if you’re also creating automatic PDF invoices, in order to have a correct number sequence.