How can I edit (cut, merge) a .MOV with video encoded by H.264 codec ?

Try Avidemux. It should handle the H264 codec just fine. When you are finished editing, just choose 'copy' under the video and audio options, so it doesn't re-encode everything. That's not necessary to do and it will save the video much faster that way too. Also, I would choose a better container format than (mov), like the (mp4) or the (mkv) container. Avidemux will let you do that too. Good luck.