How make theme css be first and not plugin css

The best way to override plugin css is with specificity. That way you only need to target the rules which you want to override.

You should also verify that wp_head(); is just before the closing tag and not before your <link rel="stylesheet" type="text/css" media="all" href="https://wordpress.stackexchange.com/questions/121639/<?php bloginfo("stylesheet_url' ); ?>" />

If you really need to get rid of the plugin’s css you can use wp_dequeue_script(); and then you would have to write your own css for the plugin.

The admin bar is supposed to show up by default unless it has specifically been overridden. To disable the admin bar for all users except admin:

add_action('after_setup_theme', 'remove_admin_bar');

function remove_admin_bar() {
 if (!current_user_can('administrator') && !is_admin()) {
show_admin_bar(false);
 }
}

Or for all users:

 show_admin_bar(false);

Your plugin might also have incompatibility issues with 3.7. It might be worth contacting them or looking it up.