it should open those ports automatically, but if it doesn't, it's 8443 for the console app, 5432 for the db (probably don't open this to public), and then 8080/8090 for server/client stuff. but unless you don't have a secure VPN, I wouldn't open those ports on your edge router anyway, unless you have a ton of mobile clients outside your network, which you could just use the cloud console to manage anyway.
According to the PDF, the minimum OS version where the console resides is Server 2008 R2 SP1 or later, so it might work on 2003, but 2003 has been dead for awhile now, so if you can upgrade that server it'd be a good idea anyways (because you haven't been getting security updates for almost 3 years now).
By high availability do you mean failover clustering? You could do that with this console like any server app really, but imo you're not well served doing it with 2003 at this point; again, security issues. doing it with VMs with Server 2012/2016 can be a bit more complex to set up initially, but a lot easier to manage...
