Thank you very much for detailed information. Usually, such issues signify that something is wrong with hardware drivers. I recommend updating sound and video drivers to the freshest version and see if it helps.
RDP connection mode doesn't work via callback connection or Internet ID. We are planning to make RDP working via those some time in the future.
What I have observed with other remote software is they normally setup there server to listen on port 80 & 443 as they know that most firewall administrators will at least allow these 2 ports for outgoing connections.
We didn't use ports 80 and 443 by default for a reason - Remote Utilities is often used not only for administering workstations but servers as well. To avoid port conflicts with server software that might listen to those ports, Remote Utilities uses port 5650.
BTW, you can change that port manually in the Host settings, if necessary.