Payment with invoice

1. In our commercial versions, yes. The system can only ask for the email of the customer if you change the "registration" option to "no registration" in the checkout tab of the configuration.

2. By default, it's a one step checkout. You can change that if you want with the "checkout workflow" option in the checkout tab of the configuration.

3. You could use the plugin "bank transfer" or "collect on delivery" and just rename it to whatever you need. You will also have to change some translation strings related to these plugins (you can do that in the config under the tab languages). You will see what I'm talking about once you try one payment with that plugin... At the end of the checkout you will have some messages related to the bank transfer or the collect on delivery...

4. Yes