Are all pixels addressed simultaneously in one frame?
There are different technologies used for &quot;computer screens&quot;.
Today's most common technology is TFT-LCD which mostly uses the Active Matrix adressing scheme to build up an image.

... is every pixel turned on during one frame?

In a TFT-LCD the pixels are on continuously, if the display has a refresh rate of 60 Hz then the pixel's brightness is updated 60 times per second.
The pixels have to be on continuously, if that was not the case (the pixel is off and dark most of the time) then they would have to be extremely bright when it is on to display an image. On a CRT this sort of happens (the dot is very bright) but the phosphors make the dot glow for some time.

How can you address millions of pixels at the same time?

It is possible but:

very expensive
not needed

Your eyes aren't that quick to respond so if all pixels are addressed in such a short time that your eyes won't notice it then there is no issue in addressing the pixels in a certain sequence.

Or is it like in CRT where it is scanned left to right, top to bottom?

Something like that indeed, but not pixel-for-pixel, instead one row (or column) is refreshed in one go. Then the next row (or colum) etc. How this precisely done  depends on the actual display.