I'd start with the camcorder's manual...
by boya84 - 8/31/13 8:50 AM
In Reply to: How to work this JVC GZ-E306BU video cam, SD card & editing? by laveenya
Then, in Macintosh OSX, use Image Capture (in the Applications directory from the right side of the Dock - assuming you use the Dock and have not changed it) to set the default behavior when the camcorder is connected and in PC connection mode. This should address Question 1.
It may be useful to have the "Detailed User Guide" from JVC, too
Page 99 shows how to copy the files to a Macintosh computer. There is a "Caution" note that says the files are read-only when the SD card is in the camcorder and connected to the computer. So what you report is expected. What I would do is copy the MTS files to the computer first... This should address your Question 2.
If your video editor can't import correctly from the files that were copied to the computer, then use a transcoder like MPEG Streamclip from www.squared5.com, convert the files to a format that your video editor prefers... This should address you Question 3.