Gumbo's answer in the Stack Overflow question How to hide the .html extension with Apache modrewrite

_ 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]