Its Okay to have your functions all in one place (file) and I like to do that in my projects and even wordpress and joomla works in this modulized way , in fact its good practice
- its good practice also to put all your files that will be included or required in separate directory and call it 'includes' for example
-to have pretty code I suggest that you have one file and lets name it 'initialize.php' and in this file you require all the files that you need to require in your project like functions and database connections and sessions ...etc and only require this file whenever you need it
-Functions processing does not consumes a lot of server processing and loading actually what makes it heavy the tons of connections you make with database , so try make them minimum as you can