Modify popular_posts_per_category function

Try this:

/**
	 * @param int $post_id
	 *
	 * @return array
	 */
	function get_posts_from_this_category($post_id = 0) {
		if(!$post_id) {
			$post_id = get_the_ID();
		}
		/** Get the category/categories that belong(s) to the post */
		$post_categories_ids = wp_get_post_categories($post_id);
		$posts               = array(
			get_post($post_id)
		);
		/** Get all posts in that/these category/categories */
		$category_posts = get_posts(array(
			"orderby"      => "date", // Actually you don't have to set this and...
			"order"        => "DESC", // ...this since it's the default value anyway.
			"category__in" => $post_categories_ids,
			"post__not_in" => array($post_id) // Exclude the current post
		));
		/** Add the posts to the output array */
		foreach($category_posts as $category_post) {
			$posts[] = $category_post;
		}

		return $posts;
	}

And if you want to display them as a list as well, call this function:

/**
	 * @param int $post_id
	 */
	function the_posts_from_this_category_links($post_id = 0) {
		if(!$post_id) {
			$post_id = get_the_ID();
		}
		$posts = get_posts_from_this_category($post_id);
		foreach($posts as $post) {
			echo "<li>";
			echo '<a href="' . get_permalink($post->ID) . '">';
			echo get_the_title($post->ID);
			echo "</a>";
			echo "</li>";
		}
	}

The only thing you have to do is creating an array with the current post in it. Then use foreach() to push the other posts to it.

Ah I see, I didn’t see you mentioning that part. Then replace the two functions with these:

/**
	 * @param int $post_id
	 * @param int $showposts
	 *
	 * @return array
	 */
	function get_posts_from_this_category($post_id = 0, $showposts = 0) {
		if(!$post_id) {
			$post_id = get_the_ID();
		}
		/** Get the category/categories that belong(s) to the post */
		$post_categories_ids = wp_get_post_categories($post_id);
		$posts               = array(
			get_post($post_id)
		);
		/** Get all posts in that/these category/categories */
		$category_posts = get_posts(array(
			"orderby"      => "date", // Actually you don't have to set this and...
			"order"        => "DESC", // ...this since it's the default value anyway.
			"category__in" => $post_categories_ids,
			"post__not_in" => array($post_id), // Exclude the current post
			"date_query"   => array(
				"before" => (array(
						"year"  => get_the_date("Y", $post_id),
						"month" => get_the_date("m", $post_id),
						"day"   => get_the_date("d", $post_id)
					))
			)
		));
		/** Add the posts to the output array */
		foreach($category_posts as $category_post) {
			$posts[] = $category_post;
		}
		/** Show all posts if $showposts is not set */
		if(!$showposts) {
			$showposts = count($posts);
		}
		/** Reduce posts according to $showposts */
		$posts = array_splice($posts, 0, $showposts);

		return $posts;
	}

	/**
	 * @param int $post_id
	 * @param int $showposts
	 */
	function the_posts_from_this_category_links($post_id = 0, $showposts = 0) {
		if(!$post_id) {
			$post_id = get_the_ID();
		}
		$posts = get_posts_from_this_category($post_id, $showposts);
		foreach($posts as $post) {
			echo "<li>";
			echo '<a href="' . get_permalink($post->ID) . '">';
			echo get_the_title($post->ID);
			echo "</a>";
			echo "</li>";
		}
	}

And call it like this, for example:

<?php the_posts_from_this_category_links(0, 3); ?>

Setting the post ID to 0 gets the current post ID. 3 is the number of links you want to display.

Excuse me, but you said “instead of starting with the most recent post in the category, it starts with the current post as most recent”. But now you want “the post preceding the current post”?

Well, then change

$posts = array(
	get_post($post_id)
);

with

$posts = array();

Glad to hear that.