Scroll down to the synthetic and game benchmarks for the 850m and see if he's getting results which are similar.
https://www.notebookcheck.net/NVIDIA-GeForce-GTX-850M.107795.0.html
Also check with a monitoring program like HWMonitor or HWInfo64 to check his GPU temps while gaming. On these Optimus laptops, if the wrong driver is installed or installed incorrectly, sometimes games end up playing on the Intel graphics. The GPU temps will tell you which GPU is actually being used (you may have to start the monitoring program after starting the game, to get it to recognize the Nvidia GPU).
Also, vsync should always be turned off on Optimus laptops. The way Optimus works is the Intel GPU always controls the screen. The Nvidia GPU acts as a co-processor. When it finishes drawing a frame for the game, the Optimus drivers transfers that completed frame from the Nvidia to the Intel GPU, and the Intel GPU displays it on the screen. So it has the same effect as vsync being on (with the vsync draw and display buffers being split between the two GPUs, instead of located in one GPU). Turning vsync on in the game could add additional lag.
Edit: For fan noise, try turning the laptop off and blasting out the insides and fan/heatsink with compressed air. Over time, dust tends to build up causing the laptop to run hotter, causing the fan to spin at a higher RPM. Clearing out the dust usually fixes it.
There's also the possibility that a fan bearing is going, and what you're hearing is vibration. The only thing you can do then is to try to oil or grease the bearing (sometimes very difficult or impossible). If that doesn't help, then you have to replace the fan. This type of noise is usually also prevalent when the fan is at low RPM.