What interaction will there be between EGL and Vulkan?
The Khronos EGL team developed Windows System Integration (WSI) extensions for Vulkan. The WSI extensions are essentially the new generation EGL to Vulkan. This may be an oversimplification, but EGL is intended to play the same role for Vulkan that it plays in the OpenGL ES world. The EGL group has historically defined the context creation and Windows system interface for OpenGL ES.
In Vulkan, it was decided not to separate WSI from the API quite so strictly. Instead, WSI is defined by a series of extensions to Vulkan, rather than a separate API. Khronos had extensive conversations with Google and Android and other platform owners in order to ensure the mechanism works well across multiple APIs, including Windows. The bottom line is that there is no EGL for Vulkan, rather WSI in Vulkan is handled by extensions.