how to show the full post: http://codex.wordpress.org/Customizing_the_Read_More#More_about_.24more
I want all the things I get in single.php
possibly copy all the code from within the loop of single.php into the loop of your random post.
my custom code … doesn’t work in index
the in_category() code might only work within the loop or needs refining – http://codex.wordpress.org/Function_Reference/in_category