Giyu survives in the manga. The plot doesn't lead to his death. His character has many adventures and developments that keep him alive and active in the story.
Nezuko is initially 12 years old in the manga. As the story unfolds, her age doesn't change significantly in a traditional sense, but her character development is quite remarkable.
Their relationship can be developed through shared experiences. For example, if they both get injured in a battle and have to rely on each other for survival while waiting for help. This would force them to open up and communicate more, breaking down Giyu's usual stoic exterior and allowing Shinobu to see a more vulnerable side of him.