In the future(2019-2020), if the American portion of the ISS had an unstable hull breach or worse a sick astronaut and 4 people took to earth. Are Russians qualified to handle the American portion of the ISS? Since they depend on the American power supply.
The international partners of the ISS look after the parts of the station they made. This is done from the mission control centers on the ground. All ISS systems are monitored on the ground and are adjusted from there, usually the crew is only involved when maintenance and repairs are needed, or new components are being installed.
So, if an extremely unlikely incident incapacitated everyone except the Russians and they all left, Houston would continue to run the US orbital segment just as they do now. This service shows some of the readouts from the consoles at the Johnson Space Center. If they needed the remaining crew to help them, they would talk them through it. Cosmonauts tend to have an engineering background and speak English, and would already be familiar with the US side. It wouldn't be a problem.
It is hard to imagine how the ISS could lose contact with the ground without all crew being evacuated. Houston would always be in touch with a crew in such a situation, and would continue to coordinate with Mission Control at Korolev, ESA, and JAXA.
If we imagine a fictional scenario like a natural disaster or a war, in which Houston can't communicate with the ISS, then the Backup Control Center takes over. That center used to be Korolev in Moscow, but has now been switched to Marshall Space Flight Center in Huntsville, Alabama. During Hurricane Rita in 2005, Korolev was used to control the ISS for a brief time, but they no longer have that capability. If the BCC also lost contact with the ISS it is unclear what would happen. Continuous contact with the station would be lost if it was not possible to use NASA's Tracking and Data Relay Satellite System, and would be restricted to when the station is in view of a ground station.