If the code in question were licensed under the AGPL, yes to all three, I would think. If you modify AGPL code and redistribute it or offer its services over a

If the code in question were licensed under the AGPL, yes to all three, I would think. If you modify AGPL code and redistribute it or offer its services over a network, you've created a derived work which is not solely 'your source code'. What you need to provide is the collective including the modifications. You can avoid this by not using AGPL licensed code.