In short: no. There's a concept accepted amongst most professional historians called historicism, which is the idea that the past and the present are different and that events arise out of their specific contexts. Place, time, culture, people and sometimes just chance are all important factors in the unfolding of events and there are always important differences between past events and the events of the present or the future. I don't think any respected historian would seriously try and predict the future.

I wouldn't necessarily characterise history as a 'chaotic jumble', though. Events arise out of previous events, it's simply that there are no universal laws for how things play out.

In my opinion no, people who say that history is cyclical generally do not have enough knowledge to make accurate judgments. As an example, during the Nara period in Japan (710-94) the Japanese assiduously imported everything Chinese from clothing, to medicine to religion, to poetry to Confucian bureaucratic systems. During the later Heian period from 794-1185 Japan entered a period of cultural isolation where they cut themselves off from the mainland and there was little to no contact with the Chinese. Consider also the Nanban trade (the time between the arrival of Europeans and their exclusion from the islands with the Seclusion edicts) from 1543-1613 which was a period of cultural exchange where many European forms of shipbuilding, weapon making and Catholicism were introduced to Japan. Japan remained officially closed to Europeans until Commodore Perry visited in 1852. Superficially each look somewhat similar. Japan goes through an intense period of change during which many new forms, technologies and ways of life are promulgated after which the country begins to look inward and excludes foreigners.

Personally I cannot bring myself to believe that these periods have anything more than a superficial similarity, the differences between these two periods of Japanese history could not be more marked. Heian Japan was relatively peaceful with a (relatively) strong central authority in the Fujiwara clan, the nobility was united, the feudal system had not developed properly, warriors were abhorred and so on. The roughly Edo period Japan had little central authority, a well developed feudal system and a warrior code in the form of Bushido. I know I've mashed up several complicated bits of history together, if there's anything that is not clear please feel free to ask.