Indeed, Black Flash was the one to defeat Savitar. The battle was full of action and unexpected twists, but in the end, Black Flash emerged victorious.
The way Flash defeats Savitar in comics involves a lot of factors. He figures out Savitar's patterns, discovers a hidden flaw in his powers, and then strikes at the right time with maximum speed and precision.
Maybe in the fanfiction, Flash discovers Peter's identity in a very unexpected way, such as seeing Peter's Spider - Man suit by accident. He then has to decide whether to keep the secret or not. He might struggle with his own jealousy towards Peter and the newfound knowledge. If he decides to keep it a secret, it could lead to an unlikely friendship between them, with Flash helping Peter in small ways without Peter knowing it's him.
Yes, there are several. You can check fanfiction websites like Archive of Our Own. Just search for 'Barry is Savitar' and you'll find a variety of stories with different takes on the concept.