How to display recent posts on home page with title, post date, author and featured image?

The functions you are looking for, are:

the_post_thumbnail_url(); // For featured image
the_author(); // For author name
get_author_posts_url(); // For author link
the_date(); // For post's date

So, your code should be something like this:

<div class="cs-post-carousel-layout">
    <div class="cs-container swiper-container">
        <div class="swiper-wrapper"><?php

            // define query arguments
            $args = array(
                'posts_per_page' => 5, // your 'x' goes here
                'nopaging' => true
                // possibly more arguments here
            );

            // set up new query
            $tyler_query = new WP_Query( $args );

            // loop through found posts
            if ($tyler_query->have_posts()) {
                while ( $tyler_query->have_posts() ) {
                    $tyler_query->the_post();
                    //Post item -->
                    ?><div class="swiper-slide">
                        <div class="cs-post-item">
                            <div class="cs-post-category-icon">
                                <a href="https://wordpress.stackexchange.com/questions/269933/<?php the_permalink(); ?>"></i></a>
                            </div>
                            <div class="cs-post-thumb">
                                <a href="<?php the_permalink();?>"><img src="<?php the_post_thumbnail_url();?>" alt="<?php the_title();?>"></a>
                            </div>
                            <div class="cs-post-inner">
                                <h3><a href="https://wordpress.stackexchange.com/questions/269933/<?php the_permalink(); ?>"><?php the_title();?></a></h3>
                                <div class="cs-post-meta cs-clearfix">
                                   <span class="cs-post-meta-author"><a href="<?php echo get_author_posts_url(get_the_author_meta('ID'));?>"><?php the_author();?></a></span>
                                   <span class="cs-post-meta-date"><?php the_date();?></span>
                                </div>
                            </div>
                        </div>
                    </div><?php
                }
            }
            // reset post data
            wp_reset_postdata();?>
        </div>
    </div>
</div>

I also reformatted your HTML code for you, and added indentation.