Of course it's possible, that's what video is for
You are working on a PC, so there is a myriad 'free' programs out there for you to test.
Sony Vegas and Pinnacle are two easy to use and accessible programs. They will be able to import straight from the camera and can edit HD content. As for a sound track, you can just layer a soundtrack (many if you like) over the movie content.
Be aware that HD files are big and if you apply any filters/effects, that they will need to be rendered and this can be quite expensive for the processor. Don't expect it to happen quickly, unless you've got a monster PC (or a Mac).