In simple terms, there's a chemical in the cells of the retina that turns light into nerve impulses. It gets used up doing so but is constantly being regenerated. With bright lights too much gets used and it takes a while for the regeneration process to replenish the stock before those particular cells can respond properly to light again. In the meantime the nerves from those parts of the retina transmit random signals to the visual part of the brain.

Are you talking about the "leftover" spots after you look away from the bright thing?

The technical term for this is an afterimage. It's mostly caused by your brain compensating for the bright stimulation of the light. Basically, your brain is looking for contrasts, and it assumes that most of your visual field "should" be at a similar brightness, so it adjusts very bright spots down in brightness in a way that lingers for a short time. (Another, smaller, contributor is that the cells in the retina - the light sensitive part of your eye - can only be stimulated so often, and a very bright light can easily saturate all of those cells so that they're effectively "disabled" for a few seconds.)

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I have no idea what you're talking about. If I look at photos of the sun sometimes I see orbs stretching out from it but I don't see them normally. What should I do to try seeing them?