OK. Firstly, you should've been prompted by the programme to activate your MPEG2 codec as soon as you tried to use it. This is done online instantly through the programme. Try clicking the 'Help' icon on the top options bar, and look through the list.
Also, try this possible solution: Download Quicktime.
What is the source, video bitrate and audio bitrate and samplerate of the mpg video?
For mov files you should not be having a problem importing the files as you ahve Quicktime installed - unless it is a very old version in which case install the latest version.
THe source is from a JVC GY-HM100U and is in native .mov format for FCP which produced an MPEG 1/2 files but I converted it to MPEG 4 and all is well. Also changed the file format on the camera to native MP4 so that will do the trick. THe MP4 format play in all media players and goes into Pro X 4 just fine and they playback great and look fantastic. I do have the latest Quicktime Pro installed and even Quicktime could not play the files with an image but worked perfectly with the MP4 format so the change in file format on the camera with solve this.