Front end post delete error confirmation and success message

There are two questions here. For styling alerts/modals, that’s a generic HTML/CSS question – check out these to get you started.

For the second, it depends what you’re doing after the delete – are you redirecting back to the frontend, or staying in the admin? (I will update my answer following your response).

You shouldn’t be reinventing the wheel – use the core function get_delete_post_link to get the delete URL. This will handle nonces and any future changes to core, if and when they occur.

Update: For your redirect, add a param that you can then check for on page load:

$redirect = add_query_arg( 'success', 'true', $redirect );

And then in your template file:

if ( ! empty( $_GET['success'] ) ) {
    echo 'Wahey!';
}