Which of these figures (Gilgamesh, Odysseus, Oedipus, Jesus, Laval, Beowulf, Sir Gawain) would you consider to be contemporary heroes? Why or why not? Also, how do the concepts of fate differ in the stories of these figures?

Of the characters listed, only Laval is a contemporary figure, occurring in the Legends of Chima, a contemporary television series. Jesus is not a "hero" per se but a religious figure. Gilgamesh, Odysseus, and Beowulf are epic heroes whose narratives are found within oral traditions, while Oedipus is a tragic hero encountered in several ancient Greek tragedies. Sir Gawain is a heroic protagonist of Arthurian Christian romance. All of the figures mentioned (other than Laval) are found in works dated between approximately 3000 BCE and 1400 CE and thus are not contemporary.
Fate is an important concept in Greek tragedy. Oedipus is unable to avoid his fate because of an ancestral curse. No matter how much Laius and Oedipus try to evade the consequences of the curse, their fates are inevitable. Fate plays some role in the epics, often with the death of a hero resulting from a fate that either could not be avoided or could only be avoided at a cost that would be unacceptably great. Often someone is fated to be a hero or to die a certain type of unavoidable death, but fate is not absolute. In Beowulf, for example, wyrd or destiny is an important concept, but courage can allow someone to successfully face down wyrd on occasion, although the existence of the concept allows a level of acceptance of death that is less common in contemporary writing.