Do channels overlap in multiple remote controls for outlets?
From the manufacturers manual that you provided, individual receivers can be "linked" to 1 of the 4 buttons on the transmitter.  This gives you the option to assign multiple receivers to a single button.  The Master button turns on/off all linked devices.

Linking is how the transmitter stores unique IDs in the EEPROM which maps the transmitters buttons to the corresponding receiver(s).

You should not have any problems with cross-communication with your dad's remote or receivers.

You may have a rare problem with signal collision if both transmitters are being used at the same time and are within close proximity.  This might result in neither working at all until one or the other has stop transmitting.