What does the "Dark age" mean in Shin Sekai Yori?
My question is, which time period does the "Dark Age" correspond to?
  
  Is the following time scale correct?


Your timeline is correct. The Dark Ages correspond to the period following the PK wars during which the slave dynasties held power (in northeastern Asia, anyway). In more detail:


Ismailov conducts his experiments in 2011, leading to the creation of the first psychokinetiker.
Psychokinetikers and ordinary people coexist peacefully, if uneasily, for a short time - perhaps a year or so? The exact duration isn't made explicit.
Boy A and people like him start using PK to commit severe crimes, prompting the formation of powerful anti-PK movements worldwide. In response, PK users band together. Some of the groups of psychokinetikers become heavily radicalized and commit acts of terrorism.
The PK wars begin. The war effort is particularly effective in the US, which almost manages to wipe out all the psychokinetikers within its borders (PK users decline from 0.3% of the population to a mere 0.0004% of the population - a few thousand people at most). 
Faced with this grave threat to their existence, the few remaining PK users develop tremendously strong PK in a short period of time. Using their newfound strength, the psychokinetikers topple every standing government on the planet. 


The collapse of all governmental structure marked the beginning of the Dark Ages, so named because - like the "original" Dark Ages that followed the collapse of the Roman Empire - little was known about it. The "new" Dark Ages lasted roughly 500 years. During this time, global communication networks collapsed, and so little was known about what was going on elsewhere in the world. The slave dynasties rose and fell, eventually leading to the rise of Saki's society.


  Also, what is known about the dark age?


Unfortunately, there isn't much known, what with it being a Dark Age, and all. In the novel, the false minoshiro does go into more detail about the four groups (and I can update this answer to include that information if you'd like). 

That said, our knowledge of the Dark Ages begins and ends with the false minoshiro. The Dark Ages were hundreds of years out of living memory by Saki's time (even for telomere-manipulators like Tomiko), and it seems that all record-keeping was effectively delegated to the libraries - that is, the false minoshiros. It seems very likely that if you were to ask the people of Kamisu 66 about the Dark Ages, they would know virtually nothing about it - perhaps not even that the Dark Ages happened at all.