I would like to know whether there is any relation between focal length and distance. For example, what is the max distance I can shoot from a 55mm-300mm lens?
The minimum and maximum focus distances have no direct relation to the focal length of the lens. All lenses have a minimum focus distance. For Macro lenses this is closer than for normal lenses (is the main part of what makes them Macro).
The majority of lenses have an infinite maximum focus distance (focus at infinity). Under certain conditions however, such as the use of extension tubes, it can become impossible for the lens to focus at infinity. In this case, there would be a maximum focus distance determined by the limit of the distance the lens can move the focal plane away from the camera and would be a distance less than the hyperfocal distance.
Your question makes no sense. The max distance for all normal lenses is infinity. The focal length will only determine the view angle at infinity, not whether you can reach infinity or not.
Pretty much any lens can focus at infinity, so I think to make sense, the question must mean maximum distance so that the image of subject is a usable size instead of a dot. Which is going to be hard for anyone else to judge, but a Field Of View Calculator should answer for individual purposes.
The Field Dimensions are the size of the distant area that the camera sees. Enter a focal length and sensor size, and it will tell you field of view size for your distance. Or tell it your desired field size (dimension or angle) and it will tell you distance.