Can low speed shutter like 20sec in "Bright Light Condition" Damage the Camera? "Bright light condition" mean artificial lights and Indirect sunlight. Just like a picture tooked in a bright room with 20sec shutter and the result is "one color white picture because high light!"
If you are talking about normal lighting conditions, then overexposing a photo that results in a totally white image will not damage a camera. After all, if there is any pure white in a scene, that spot on the sensor is totally saturated when properly exposed. Such an exposure does not damage the spot on the sensor that records the pure white, does it?
If you are using a mirrorless camera, other than the very brief times when the mechanical shutter closes/opens to expose the image/closes/reopens to continue Live View, the imaging sensor is exposed to light for the entire time the camera is turned on. Under very bright daylight conditions the camera is not damaged even after many minutes of continuous use. The same is true with shooting video. Even in very bright conditions the sensor is not damaged when exposed to light for several minutes or even hours.
Where you will get into problems is if an extremely bright direct light source, such as the sun or a powerful laser, is inside the camera's field of view. In that case it might not even take a long exposure to damage the camera. Lasers with enough power can damage a sensor almost instantly.
Damage from pointing the camera at the sun is usually heat related and takes a bit longer. Longer focal length lenses, which concentrate more of the sun's energy, can contribute to major damage:
With wider angle lenses and a camera with a mechanical shutter that covers the sensor at all times except when the image is actually exposed, it is possible to take images that contain the sun in the field of view without damaging the camera. Be very careful not to look directly at the sun in the viewfinder, though, as the sun can damage your eyes!
You are mixing few things together. First, take a look at the exposure triangle. What is shows is that amount of light hitting your sensor, depends on exposure and aperture. Smaller apertures (f-number 22) will let in less light. Longer exposure will let in more total amount of light.
Now, sensor can be damaged by very intense light, just like any material. Exposure is only part of equation, for example, you might be OK with 20 second exposure when aperture is very low. On the other hand, short exposure can let in enough light to damage the sensor when aperture is open.
From this question, it seems that if you shoot sun directly (or sun eclipse) at 1/4000 shutter speed and f22 aperture, you can actually damage your sensor. So don't do it.
What also is important is not just amount of light getting into camera, but how fast it gets there. In other words, your 20 second exposure with small aperture can get in a lot of light, but over longer period, allowing camera to cool down, hence lowering chance of damage. Damage to camera is a sum of heat in versus heat out.