Using a .php file in a frame will work fine.
Your second question, frankly, doesn't make sense. There is no such thing as a "PHP site" or an "HTML site". They are two different technologies, designed to perform two different tasks, which complement each other.
HTML, as you know, is a markup language, designed to describe the structure of textual data.
PHP is a programming language - that is, it executes logical instructions - which is used to generate HTML on the fly, usually by reading from or writing to a database, processing that data as necessary, and producing appropriate an appropriate result - in the form of HTML code - to display to the user.
If your web server supports PHP, you can use PHP files on your site.