obviously it's the shortest and cheapest way.Really? I suspect that the direct highway bus is fasteer and cheaper.
I would like to know how far is the harbour from kumamoto to city?
20-25 minutes by bus.
When i arrive at Shimabara port how will i get to Nagasaki?
By train via Isahaya (from Shimabara-Gaiko Station near the ferry terminal to Nagasaki Station). You can look up train fares and timetables here:
http://www.jorudan.co.jp/english/norikae/
Is the harbour far from Nagasaki railway station?
Shimabara Port is almost a two hour train ride from Nagasaki Station.