With both the angels and humanity, God chose to present a choice. One third of the angels choose to follow Satan in his rebellion, becoming the fallen angels-demons. Unlike humanity, however, the choice the angels had to follow Satan or remain faithful to God was an eternal choice. The Bible presents no opportunity for the fallen angels to repent and be forgiven. Nor does the Bible indicate that it is possible for more of the angels to sin. The angels who remain faithful to God are described as the "elect angels" (1 Timothy 5:21). The Nephilim could have been the "giants" that were destroyed by the Israelites during their invasion of Canaan (Joshua 11:21-22) and later in their history (Deuteronomy 3:11; 1 Samuel 17).
They do not have free will. They were created in the time where free will was, well, still a new thing. It wasn't necessary for them to have it. Extinct? Umm, last time i checked, they're still around. I'll go ask my Seraphim friend if her buddies are extinct. Her name is Sally!
It's not unreasonable to believe angels were created with free will when we consider that we humans were created with free will (Luke 22:42). As for the Nephilim they were destroyed in the flood (Genesis chapter 6).