It is indeed a rule that comes from film cameras.

On point 4 the answer is simple:

Multiply the focal length with the crop factor of your sensor. Because the sensor is smaller than a full frame sensor, it will not cover the full image circle, cropping out a smaller image. This has the effect of looking like a longer focal length.

E.g. on Canon, a 50mm lens from full frame has a rule of thumb of 1/50s. On a Canon crop sensor, with a crop factor of 1.6, this reduces to 50*1.6 = 80 hence a recommended shutterspeed of 1/80s.

Point 3 is bit more tricky:

I hope you are familiar with the concept of stops. Double or half the exposure = a difference in one stop. IS is described in stops. e.g. IS that gives you two stops should allow you to handhold your lens for an amount of time 4 times as long as without IS. Of course it requires you to be reasonably steady, as IS can only do "so much".

Point 2: Yes, but you shouldn't aim for blurry photos anyway.

Point 1: Yes and no. A higher resolution sensor will resolve the blur more clearly, but it isn't blurred more. More pixels cover the same area, hence, when viewing an image at 100%, you will get the impression of more blur, though the blur is identical. The resolution of the "other sensor" was just too low to resolve it.

To give you an absurd example:

If you had a camera with 1 pixel, it would never show any blur - because it cannot resolve it.