In the footer.php file of my theme, I'm going to get the php variable of the current post's category - is this possible? Thank you.
Yes. Within the loop, run WP's category function and assign it to a variable. Then, in the footer, you can echo the variable or do whatever you want. Done it once before, from memory get_the_category() is the one you want.
It's get_the_category(). It returns all the categories of the post in an array, so you have to loop through it.