I would suggest using the org.geotools.referencing.datum.DefaultEllipsoid.WGS84.orthodromicDistance() method. See, for example, it's use in the OSMImporter at https://github.com/neo4j/spatial/blob/master/src/main/java/org/neo4j/gis/spatial/osm/OSMImporter.java#L2158
And in response to the secondary question about finding the closest Geometry to the point, take a look at the utility method findClosestEdges at https://github.com/neo4j/spatial/blob/master/src/main/java/org/neo4j/gis/spatial/SpatialTopologyUtils.java#L102. This will return a collection of PointResult, containing the closest Point and the Geometry it belongs to. If you review the code you'll see that it uses JTS class LocationIndexedLine to calculate the closest part of an edge.