To rule of LTPA issues. Login to your dwa server and access the names.nsf. After authentication, switch the domain name to the same time server and try to acess names.nsf. If you are prompted to authenticate, then LTPA is not working and needs to be configured correctly. Also, try to use the fully qualified host name in the url, not ip or just local host.
For the stlinks issue. Check the doc below. That explains the configuration steps between a https Dwa server and a non ssl sametime server.