Purpose is generally specific to what the author wants the work to do or what cause they are promoting.
Function seems to include hindsight. For example we can look back and say "The History Of Everything functioned as a guide to the study of history in the 17th century" (function), whereas you can also say "In The History Of Everything, author Random J Historian intended to create a comprehensive work which demonstrated the positive effects of religion in society" (purpose).
Bias and perspective are very similar, however, perspective tends to describe a mental position or background ("From the perspective of a 19th century English philosopher") whereas bias more often refers to a particular opinion/inclination ("He was biased against Marxist thinking").
Form I'm not so sure about, perhaps refers to the writing of history and the way in which historical texts are constructed, ie, is it a narrative, is it a chronological history, is it an exposition on a particular topic, is it a series of biographies from the time.