In hybrid mode the default GPU is Intel. Nvidia-settings is designed to work in Nvidia mode only. Additionally, you should not use it with optimus-manager! The reason for it is, that optimus managers uses own configs in different location for each driver mode, so the usual configs must be disabled so they wouldn’t interfere. When you save settings with nvidia-settings, it writes them to the usual config, if not present, it creates a new one, which is conflicting with optimus-manager. So if you did this, check your graphical configs according to tutorial once again and disable them.
You can still manipulate Nvidia config but manually and you must know which one is from optimus-manager.
Please, read the optimus-manager documentation, especially Configuration:
As to the lag on the other monitor, I can’t help much. Each monitor is different and reacts differently to software and settings. Laptop monitors are somehow standardized. When you attach different screen, it is most likely that it will have different refresh frequencies tied to different resolutions.
You must also know that rendering additional screen is using more resources than one screen. You can see this when running a game. With secondary screen, FPS count drastically drops.
I don’t know how GPUs are handling multiple screens, but from what I see, they cause issues. For example, on my laptop all is fine and I don’t have any screen tearing, while on secondary screen is huge, so I basically can’t run any videos there. Maybe it’s because it tries to use the same frequency that is meant for laptop screen? I don’t know. Use xrandr utility (or arandr for GUI, but commandline is more powerful, see some articles about xrandr) to check your monitor properties and what settings are being used. Maybe if you tweak them for secondary screen, lag will be gone?
Multiple monitors is a headache. Especially when you try to use TV, which is way worse and less recognizable by drivers, so things may not work as expected, because many TVs were never meant to be used on computer.
It is possible that for such setups something must be added to driver configs but since in hybrid mode you use Intel modesetting (probably), you need to tweak configs for Intel modesetting, not Nvidia ones. If you switch to Nvidia mode, Nvidia probably is better suited for such situations, hence the better behavior.