As the title says, has Japan ever gone through a "Dark Ages" similar to Europe? In addition to Japan, has there been a time period like this in Southeast Asia? Thanks in advance!
If by "Dark Ages," you mean a period when central authority is gone then one can make the argument that late Heian fits the bill since the government and the aristocrats in Kyoto lost control of the country with bandits everywhere starting around 900-1000.
A weak central authority was reestablished with the Kamakura shogunate starting in 1192, but it didn't last long. The return of a strong central authority would have to wait until Hideyoshi's unification of Japan in 1591 (except for Ashikaga Yoshimitsu's brief period after he unified the Northern and Southern courts in 1392 and died in 1408).
If by "Dark Ages," you mean a period when big cities collapsed and "civilization" (however you define it, regressed) then it doesn't quite work because Japan had very few big cities and Kyoto remained a major city and was the cultural center of Japan until at least the 1600s.