Does the latest beta include the ability to upload a cover image / featured image

You can modify “question CPT arguments” in post_type.php

path:  anspress-question-answer\includes\post_types.php

about line 69

$args   = array(
			'label' => __( 'question', 'anspress-question-answer' ),
			'description' => __( 'Question', 'anspress-question-answer' ),
			'labels' => $labels,
			'supports' => array(
				'title',
				'editor',
				'author',
				'thumbnail', //add this thumbnail
				'comments',
				'trackbacks',
				'revisions',
				'custom-fields',
				'buddypress-activity',
			),

and you can upload thumbnail at wp-admin new question page.