This page explains how to use Fill PDF to solve the various problems it was created to solve.
Attach the PDF to an e-mail after it's filled and send it
This is possible by using the default Rule that comes with Fill PDF. You need Rules, Webform Rules, and Mime Mail for this to appear. You sometimes have to use the development version of Rules's data conversion features and a bit of PHP to get the tokens and variables you need so everything will work, but it is possible to set things up as you need.
This is being improved (see #1266174: Rules integration).