You might be looking for this part of the UiPath documentation?
So to answer your questions;
Only standard ports 443/80 are used for communication
If you do not have an internet connection (assuming that’s what you mean by “private”), the robot (assistant) is not able to connect to UiPath Cloud. However if your server is connected to the internet usually following applies; if above mentioned ports are not blocked and the services listed in above link are not blocked, assistant should be able to establish a connection to UiPath Cloud and run automations.
Hope that answers your questions and happy automating.