Displaying the first, second, and third posts from a category in separate slides

You should use WP_Query() instead of query_posts. You also don’t need a separate query to loop through for each one. Just use a WP_Query for the Featured category, limit it to 3 posts, and you should be good to go. It’s not necessarily optimized but I cobbled it together with your code sample.

This should get you started:

<?php
    $per_page = 3;
    $slideshow_query = new WP_Query( array(
        'cat' => 1,
        'posts_per_page' => $per_page,
    ) );

    if( $slideshow_query->have_posts() ){
        echo '<div class="slideshow-container">';
            while ( $slideshow_query->have_posts() ) {
                $slideshow_query->the_post(); ?>
                <div class="mySlides fade">
                    <div class="numbertext"><?= $slideshow_query->current_post + 1; ?> / <?= $per_page ?></div>
                    <a href="https://wordpress.stackexchange.com/questions/295382/<?php the_permalink(); ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>">
                        <?php the_post_thumbnail( 'large' ); ?>
                    </a>
                    <div class="text"><?php the_title(); ?></div>
                </div>
            <?php } ?>
            <a class="prev" onclick="plusSlides(-1)">&#10094;</a>
            <a class="next" onclick="plusSlides(1)">&#10095;</a>';
        </div>
    <?php } else {
        _e( 'Sorry, no posts matched your criteria.' );
    }
?>

Update: with a recent edit it should be noted that

<?= $slideshow_query->current_post + 1; ?> / <?= $per_page ?>

is functionally equivalent to

<?php echo $slideshow_query->current_post + 1; ?> / <?php echo $per_page ?>

<?= is known as the Short Echo Tag

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