how do I encode links to specific archive searches? in WordPress

WordPress can generate these, so you can too. You would need to use the same function that WordPress does.

For category it would be something like:

$category = get_category_by_slug( 'example' );
$link = get_category_link( $category->
term_id );

Similarly there is get_tag_link() and on deeper level they all really use get_term_link()

I didn play much with authors, but there is the_author_posts_link() and probably some get_ analogue.