How to merge or move two vertices without affecting the others? I want to merge two vertices into one, but Blender help me to select the third one automatically. I didn't turn one Proportional Editing Mode. Would anyone here can explain why? Please go to my shared videos below to see my problem in detail, if my word is not clear enough. Thank you

https://drive.google.com/file/d/0B7o5ywq5dlOgOFNVVHhkZzljcjQ/view?usp=sharing
As I see, you are using Ctrl + mouse click instead Shift + mouse click  for selecting multiple vertexes.  Ctrl + mouse click is a Pick Shortest Path function and select road from vertex to vertex.

To add vertex to selection use Shift + mouse click