The problem is your shutter speed is too fast for the type of lighting you have. Most LED lights flicker (and fluorescents, in a slightly different manner and degree) at either 50/60 Hz, or 100/120 Hz, depending on the mains frequency where you live.
At a shutter speed of ¹⁄₄₀₀ second, it's a bit of a crapshoot whether your shutter will be timed with the peak of the light's output. For instance, in your 3rd and 4th photos, look at the TV's shadow on the wall. In the 3rd photo, the light was increasing in intensity as the shutter traveled across the image sensor (remember, the image enters the camera from the lens upside-down, so the bottom of the photo was the first to be exposed). The top of the photo is clearly brighter — therefore as the shutter traveled from the beginning of the exposure to the end of the exposure, the lighting became brighter.
In the 4th photo, the lighting was decreasing in its flicker pattern. Again, the bottom of the photo is brighter, which is counter-intuitive for lighting coming from the ceiling. The shutter exposed the top of the sensor (corresponding to the bottom of the image) first, and as the shutter traveled, the ambient lighting was falling.
Solution: slow down your shutter speed to something like ¹⁄₂₅ or ¹⁄₃₀ of a second (¹⁄₂₅ if you have 50 Hz AC mains frequency, ¹⁄₃₀ if your AC mains are 60 Hz). This will allow for two or four complete flicker cycles, smoothing out the lighting. Of course, you'll have to compensate by either decreasing your aperture or decreasing your ISO by 4 stops, or some combination of both to account for the +4 stops of shutter exposure.
You could expose at ¹⁄₅₀ / ¹⁄₆₀, which would allow for either one or two full cycles (again, depending on the specific type of LED light you have). And of course, your total aperture/ISO compensation would only be by 3 stops (relative to your settings when you shot at ¹⁄₄₀₀).
You could also do some testing to determine if your flicker is at mains frequency (50/60 Hz), or at twice mains (100/120 Hz), by taking lots of shots at ¹⁄₁₀₀ / ¹⁄₁₂₀. If you never see any variable lighting when shooting at that rate, your LEDs probably flicker at 100/120 Hz. If you do see some darker photos, then they probably flicker at 50/60 Hz, so you should drop your shutter speed to allow for at least one full cycle of the lighting.
At least 2 full cycles is probably better, to ensure much more consistent and predictable results. The camera's shutter timing isn't necessarily so precise as the mains frequency.
Most of the following questions pertain to fluorescent lighting, but many of the answers cover much of the same territory, and and ultimately boil down to the same reason — flicker due to AC line frequency.
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