If you configure your certificate in the Load Balancer there's nothing to configure on the Apache available in the WP instance. You just need to change the domain name in WordPress (I think you already did that).
What do you mean with that? Do you mean that it allows you to access using both http and https or do you meant that your browser throws you an error alerting you're accessing an insecure site?
Could you share with us your website domain so we can see the error?