HTTPS on Amazon EC2 instance

I have a question which I hope somebody can answer for me.

My situation: I have an Ubuntu Server running Apache2 on a EC2 Amazon instance, which is serving an OwnCloud instance.

My goal: I want to deploy HTTPS on this instance. I already configured the security group to allow HTTPS traffic from anywhere (as the server should be accessible from anywhere on the internet). We already have a domain name bar.com registered at another domain hosting company. But we want to point foo.bar.com to this owncloud installation.

My questions:

1) Which IP-address do I use to configure the DNS at this domain hosting company. Because the public ip-address and public DNS of the EC2 instance is renewed every time the instance restarts.

2) How do I generate the SSL certificate for HTTPS configuration of Apache2? More specifically, which common name (CN) do I need to put in the certificate. Because the public dns of the EC2 instance is changing on every restart. I think if I put the foo.bar.com CN in the certificate that the browser will throw a certificate error once the user gets redirected from foo.bar.com -> .compute.amazonaws.com, am I right?

In short: how do I deploy https on a EC2 instance at Amazon AWS with a dns at a third party domain name service?