There are quite a number of video editing programs available. I suggest taking advantage of the free trials of a couple of them, or more, to find one you like to work with.
Here are three examples:
Sony Vegas Movie Studio Platinum HD
Corel VideoStudioÂ® Pro X4
Adobe Premiere Elements 9
You can burn high definition video onto dvd disks, but not all players will recognize it. AVCHD is one type of high definition video that was intentionally designed to play from blank dvds, rather than blu ray, so this may be one type of output for you to use. (and it shows up in the manual for your player as a compatible format)
I know that the Corel program can work with AVCHD, but I'm not sure about the other two. (Edit: looks like the Sony program can also) The downside to burning HD video onto dvds is that you don't have nearly as much room.
Hope this answers a few of your questions. Welcome to the forums.