Re: in a line parallel and close to [definition for along?]
Yes, along is implicitly horizontal. It will also include a slight vertical element (e.g. along the hilly road) and it becomes a matter of judgement when along becomes "up/down". It is usual that along implies a greater distance than the width of the thing that you are travelling "along." It is also a matter of judgement when "along" becomes across. E.g. "Measure it along the left side" "Measure it across the left side."
"There are no rules in English, only guidance. Some guidance looks like a rule; it probably isn't."