Is it safest for a group of cyclists to ride in a single line? Is it required for cyclists to ride in a single line in a narrow bike lane, or can they pass on the left in open traffic?
In general it depends on the road or trail, how wide it is, how straight or twisty, how visible the trail ahead is etc.
On a wide trail without tight turns and plenty of forward visibility riding two-abreast is fine.
On a narrower trail with tighter turns or less visibility, riders should ride single-file and stay on their side of the trail. Common sense applies to overtaking, i.e., don't try to pass if you can't see far enough ahead.
There may be laws that apply to cyclists in different locations of course.
This depends very much on the situation, and on local law.
For example, suppose the road isn't wide enough that a car can safely pass a bike. In this case, it may be better to ride two-abreast because that makes it impossible for cars to pass, whereas riding in single file might result in some cars trying to make unsafe passing manoeuvres.
Conversely, if the road is wide enough to allow cars to safely overtake a single bicycle but not two bikes side by side, it's likely to be safer – and more polite! – to ride in single file.
I assume you're referring to a pace line, where riders take turns on the front.
You'd think a dual pace line is wider than a single paceline, but with a single there's almost always a rider drifting to the back, either on the left or the right. So effectively they're the same width most of the time.
A dual paceline has two columns of riders, so blocks each other's view to some extent. But a single line has a larger differential in speed between the column and the single, so its a higher relative passing speed.