Since they are reflections, they will move in a perhaps non-intuitive way as your relationship to the light source changes.
Yes, it becomes more obvious as cameras get better.
I posted this photo several posts back; it's a still from a Hallmark Channel movie shot with a cinema digital camera and lens that costs well over $40,000:

However, you typically will not see flare from the old 640x480 camera on an old cell phone from 1995 because the lenses are garbage.
In between, the flare may be there but it won't be as obvious as it is from a better camera.