Looks good. You need to make a new handle for it or repair the old one with some new wood. After all this is a practice saw so it be a shame not to practice making a handle. Bad Axe's or Blackburn tools' blog has some great info and links, just be careful about the rabbit hole.
I would use screws, especially if it is not visible. As for the back panels, I normally like measuring the most parts I can directly off my project. You can adjust for slight errors along the way by doing this. So I would build and then measure for the panels.
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