Can anyone access my computer?
No, by default Unified Remote only communicates on your local network. I.e. there is a direct connection between the app on your smartphone and the server on your communicate. For best security make sure that you have a good router and firewall.
Note that you can configure your router to allow Unified Remote to communicate with the outside world. This enables you to use Unified Remote from a mobile data network. However, in this case you should make sure that you enable password-protection and optionally encryption in the server settings.
We also recommend that you enable password-protection if you're computer is connected to an open network or public hotspot.