Remote access capabilities using network settings

I know enough to know that it is possible for access to be granted to someone ( not just average hacker ) using various software and settings such as those used for networking. How does it work on Broadband USB sticks? Blocking the port, firewall settings, time management? Here lately, when I go to use my brand new usb stick ( on a questionable pc but though broadband was more secure ) it takes forever, and sometimes have uninstall/re-install or repair it before it takes. The logs are filled with interesting stuff. Some I understand, some I don't. Any thoughts.