One of the popular Bucky Barnes fanfics is 'Bucky's Path to Healing'. It details his healing process from all the physical and mental wounds he has endured. The story is quite engaging as it shows his growth step by step. Additionally, 'In Bucky's Shadow' is a fanfic that tells the story from the perspective of someone who is in awe of Bucky, and it gives a different view on his character.
Sure. 'The Winter Soldier's Redemption' is a great one. It focuses on Bucky's journey to overcome his past traumas while also building new relationships. Another good fanfic is 'Bucky and the New World'. It explores how Bucky adapts to the modern world in a really interesting way.