[till]

If I remove :8080 I get an ERROR 500 - Internal Server Error!

Check the error.log of the website for the error message.

I think I can use http://webmail.clientdomain.com/ using CNAME, but I'm not sure how do that.

CNAME is a dns record, this is required because otherwise the subdomain does not exist, but that not enough to display the website. You will have to add a aliasdomain to that website for every additional domain too.