Showing “ Notice: Undefined variable:” and “ Notice: Trying to get property of non-object”

EDIT

I have rewritten your complete shortcode. I’ve tested the code from my original answer, and with your code combined, the output was a bit unexpected.

Major modifications

• I’ve removed category and replaced it with a tax_query (see WP_Query). The reason is, a tax_query can be used for build-in categories and for custom taxonomies, and custom taxonomies are usually used with custom post types

• Rearranged the structure of the query a bit to make it more workable and more readable. It is also better to debug

Please Note: This shortcode needs at least PHP 5.4

add_shortcode( 'news_box', 'newsbox_new_loading_shortcode' );
function newsbox_new_loading_shortcode($atts){
    ob_start();
    $a = shortcode_atts( 
        [
            'posts_per_page'    => '-1',
            'news_box_title'    => 'Latest News',
            'post_type'         => 'post',
            'taxonomy'          => '',
            'terms'             => '',
        ], 
        $atts 
    );


    if( '' == $a['taxonomy'] || '' == $a['terms'] ) {
        $args = [
            'posts_per_page'    => $a['posts_per_page'],
            'post_type'         => $a['post_type'],
        ];
    }else{
        $args = [
            'posts_per_page'    => $a['posts_per_page'],
            'post_type'         => $a['post_type'],
            'tax_query'         => [
                [
                    'taxonomy'  => $a['taxonomy'],
                    'field'     => 'slug',
                    'terms'     => $a['terms'],
                ]
            ]
        ];
    }
    $q = new WP_Query($args);

    if ( $q->have_posts() ) : 
        while($q->have_posts()) : $q->the_post();   
            $newsbox_post_img_src = wp_get_attachment_image_src(get_post_thumbnail_id(), '', false, '' ); ?>

            <li class="news-item">
                <table cellpadding="4">
                    <tr>
                        <td>
                            <?php if( !empty($newsbox_post_img_src)) { ?>
                                <img src="https://wordpress.stackexchange.com/questions/159818/<?php echo $newsbox_post_img_src[0]; ?>" width="100" class="img-circle" />
                            <?php } ?>      
                        </td>
                        <td>
                            <?php the_excerpt(); ?>
                        </td>
                    </tr>
                </table>
            </li>

        <?php endwhile;
        $list = ob_get_clean();

        return $list;
    endif;

    wp_reset_postdata();
}

If you need to make it compatible with PHP versions below 5.4, just change it to

add_shortcode( 'news_box', 'newsbox_new_loading_shortcode' );
function newsbox_new_loading_shortcode($atts){
    ob_start();
    $a = shortcode_atts( 
        array(
            'posts_per_page'    => '-1',
            'news_box_title'    => 'Latest News',
            'post_type'         => 'post',
            'taxonomy'          => '',
            'terms'             => '',
        ), 
        $atts 
    );


    if( '' == $a['taxonomy'] || '' == $a['terms'] ) {
        $args = array(
            'posts_per_page'    => $a['posts_per_page'],
            'post_type'         => $a['post_type'],
        );
    }else{
        $args = array(
            'posts_per_page'    => $a['posts_per_page'],
            'post_type'         => $a['post_type'],
            'tax_query'         => array(
                array(
                    'taxonomy'  => $a['taxonomy'],
                    'field'     => 'slug',
                    'terms'     => $a['terms'],
                ),
            ),
        );
    }

    update_option('_post_type_name', $a['post_type']);

    $q = new WP_Query($args);

    if ( $q->have_posts() ) : 
        while($q->have_posts()) : $q->the_post();   
            $newsbox_post_img_src = wp_get_attachment_image_src(get_post_thumbnail_id(), '', false, '' ); ?>

            <li class="news-item">
                <table cellpadding="4">
                    <tr>
                        <td>
                            <?php if( !empty($newsbox_post_img_src)) { ?>
                                <img src="https://wordpress.stackexchange.com/questions/159818/<?php echo $newsbox_post_img_src[0]; ?>" width="100" class="img-circle" />
                            <?php } ?>      
                        </td>
                        <td>
                            <?php the_excerpt(); ?>
                        </td>
                    </tr>
                </table>
            </li>

        <?php endwhile;
        $list = ob_get_clean();

        return $list;
    endif;

    wp_reset_postdata();
}

function newsbox_excerpt_more($more) {
    global $post;
    $post_type_name = get_option('_post_type_name');
    if( 'post' != $post_type_name ){
        $read_more_text = "TEXT FOR ALL THAT DOES NOT HAVE post POST TYPE";
    }
    else {
        $read_more_text = "Read More &raquo;";
    }
    return '...<a href="'. get_permalink($post->ID) . '">' . $read_more_text . '</a>';
}
add_filter('excerpt_more', 'newsbox_excerpt_more');

You can then use your shortcode as follows

[news_box posts_per_page=-1 news_box_title="Latest News" post_type="event_type"  taxonomy="event_cat"  terms="testcat"]

or

[news_box posts_per_page=-1 news_box_title="Latest News" post_type="post"  taxonomy="category"  terms="testcategory"]

or

[news_box posts_per_page=-1 news_box_title="Latest News" post_type="post"]

ORIGINAL ANSWER

You don’t need to use $post->ID when using get_post_thumbnail_id inside the loop. By default, the current post ID is used, thus unnecessary to specify an ID. Also, you will need to actually check if $newsbox_post_img_src has something to return, otherwise it will return a

Trying to get property of non-object

error. Another thing to note, you should reset your custom loop with wp_reset_postdata and output from a shortcode should be returned, and not echo‘d

Your code should basically look something like this

while($q->have_posts()) : $q->the_post();   
    $newsbox_post_img_src = wp_get_attachment_image_src(get_post_thumbnail_id(), '', false, '' );

    $list="<li class="news-item">";
    $list .= '<table cellpadding="4">';
    $list .= '<tr>';
    $list .= '<td>';
    if( !empty($newsbox_post_img_src)) {
        $list .= '<img src="'.$newsbox_post_img_src[0].'" width="100" class="img-circle" />';
    }       
    $list .= '</td>';
    $list .= '<td>'.get_the_excerpt().'</td>';
    $list .= '</tr>';
    $list .= '</table>';
    $list .= '</li>';
    return $list;

endwhile;
wp_reset_postdata();