No problem.

Updating the buddyblog_show_custom_cats to this

function buddyblog_show_custom_cats( $settings ) {
	$tax = array();

	$tax['category'] = array(

		'taxonomy'  => 'category',
		'view_type' => 'dd',
		'child_of'  => 91, //CHAGE It with the correct ID,
		'orderby'   => 'slug',
		'order'     => 'ASC'
	);

	$tax['post_tag'] = array(

		'taxonomy'  => 'post_tag',
		'view_type' => 'dd',
		'include'   => array( 1,2,3),// tag ids.
		'orderby'   => 'slug',
		'order'     => 'ASC',
	);

	$settings['tax'] = $tax;

	return $settings;
}

should do it. I have not tested it, I am hoping that it works.

replace the old function with the same name with it.

About last few issues:-
1. If you want, you can create yourtheme/buddyblog/posts.php and override the whole layout(for custom query, please see buffyblog/templates/buddyblog/posts.php)

2. Please see 1
3. You are logged in as admin. By default BuddyBlog lets admin edit post in the backend. You can control who will see edit from backend link in the BuddyBlog settings. Normal users will be doing it from front end.

Regards
Brajesh