Gumbo’s answer in the Stack Overflow question How to hide the .html extension with Apache mod_rewrite should work fine.
Re 1) Change the .html to .php
Re a.) Yup, that’s possible, just add #tab
to the URL.
Re b.) That’s possible using QSA
(Query String Append), see below.
This should also work in a sub-directory path:
RewriteCond %{REQUEST_FILENAME}.php -f
RewriteRule !.*\.php$ %{REQUEST_FILENAME}.php [QSA,L]