Companies are exclusively for the Invoice module. You are correct that Reports are not by Company. Reports are generally not used to send to the client if you are using the Invoice module. For people who do not use the Invoice module, they take the data and put it into their own system/format.
We use the built-in email functions for sending emails. It defaults to your "default email" address. We cannot change that, buy you can select a different From: email in that screen if you want.
Invoicing by company: you can set the "Meta-Characters" for each specific Company, for the Subject or Body of the email. Please see the Manual for details.