Template file not loading
I'd say best to stick with where Civix (aka Tim) says it should go! (i.e. no subdirs) - and note that Civix can help you create the page:

https://wiki.civicrm.org/confluence/display/CRMDOC/Create+a+Module+Extension#CreateaModuleExtension-Addabasicwebpage

To generate a Page:

me@civisys:/home/me$ cd /var/www/extensions/com.example.myextension
me@civisys:/var/www/extensions/com.example.myextension$ civix generate:page --help
Usage:
 generate:page className webPath

Arguments:
 className  Page class name (eg "MyPage")
 webPath    The path which maps to this page (eg "civicrm/my-page")

me@civisys:/var/www/extensions/com.example.myextension$ civix generate:page Greeter civicrm/greeter
Write /var/www/extensions/com.example.myextension/xml/Menu/myextension.xml
Write /var/www/extensions/com.example.myextension/CRM/Myextension/Page/Greeter.php
Write /var/www/extensions/com.example.myextension/templates/CRM/Myextension/Page/Greeter.tpl