Backup camcorder using Final Cut Pro or iMovie
Firstly, it's well worth upgrading your FCPX to the latest (2018: 10.4.3) it should remain compatible, costs you no extra, and is a massive improvement. Don't do this mid-project; allow yourself time to adjust.

1: Yes, FCP can archive a connected camera. It produces the .fcparch file (which is actually a bundle containing all the original video files on your camera). Basically, the .fcarch file is a clone of the video parts of the card from your camera, is roughly the same size, and the FCP X Import window can read it just like a connected camera. See "Create and Manage Camera Archives" in FCP X help.

2: If you want to backup your AVCHD camera to a NAS, just directly copy the PRIVATE folder you see at the root level of the camera card into its own folder on your NAS, which you could name after the card's number / reel number to distinguish it from all the other PRIVATE folders.