The Search API is merely a CloudSearch query url-encoded. See CloudSearch documentation for search syntax
See Service API Design for more information regarding the rationale and design details.
In responses from the service, dates are serialized as long integers expressing epoch time - the number of seconds elapsed since midnight Coordinated Universal Time (UTC) of January 1, 1970, not counting leap seconds. Here's a handy tool to convert from epoch time to human readable dates: http://www.epochconverter.com/
In requests to the service, dates can be serialized either as long integers expressing epoch time or human readable dates in RFC 3339 format such as '2011-01-31' or '2011-01-31T22:00:00'