A latitude/longitude coordinate pair only specifies a single point on the globe, and doesn't imply any details about the geography of the area around it. There may be an API that can take in a coordinate pair and give you the name of the nearest street, and then the Google Directions API could give you a set of coordinates that indicate turning points along the street (since not all streets are completely straight). Once you've got those coordinates, you can draw a line passing through all of them, and that will represent the street.
Hope that's helpful - unfortunately I haven't used the Google Directions API in a long time so I'm not sure of it's capabilities regarding this type of thing.
EDIT: This question may be helpful for the first part. The top answer links to an API someone made to find the name of the nearest street to a given Lat/Long pair. Not sure if it works in every country though.