How can I list random authors from current post category?

After you populate $author_array, you need to pick 6 random users out of it. Here are two straightforward choices:

1. Shuffle the array shuffle($author_array); and pop values off of it in a for or while lopp using array_pop()
2. Create a randomized copy of six elements of the array using array_rand($author_array,6); and then iterate through the new randomized array using foreach as you did above.

Personally I prefer #2, but please note that if you try to pick 6 random elements from an array of fewer than 6 elements with array_rand() you’ll get a warning. You’d want to test the size of $author_array with count($author_array) first to either limit your array_rand() command to the max size of the potential list of authors, or to skip it entirely if it’s 1.

Something like, after your first foreach ends:

if(count($author_array) >= 6) {
    $max = 6;
} else {
    $max = count($author_array);
}

$random_authors = array_rand($author_array,$max);
foreach ($random_authors as $author) { ...