How to create and send via email a PDF file with rules?
You should write a port to Drupal 7. The Views PDF MIMEMail module codebase is pretty lightweight (~300 LOC). Essentially, it's a 


.info file declaration
A .module declaring a theme function
Various Rules integration functions (.rules.inc).


You can figure out how to convert the .info &amp; .module by Googling around how to convert a .info to D7 and look up how hook_theme() changed in D7. There's a comprehensive guide on porting D6 modules to D7 if needed.

As for #3, the Rules module has some internal documentation that describes how to integrate Rules in D7. There's likely a few structural changes you'll need to do, but essentially most PHP code should stay the same.