I can't help with your first issue but when riveting using standard rivets the front of the rivet needs to be held tight against the front of the lock, I use a rivet set a metal rod with a cup for the rivet head to hold it tight. Wood or leather will deform and make for a loose fit.
A ball peen hammer is best for riveting but I often use a small bolt with a slightly dished end to peen over the end of the rivet as I can place it where I want it then hit it with the hammer.
I am sure you could remove the rivets and try again a tighter fit may resolve your locking issues small washers behind the rivets may also help them to grip the leather.
If all else fails would it be possible to cut a piece of leather larger than the lock mount the lock to that and stitch that to the case and make a feature of it.
Hope that helps I am not an expert but have had similar issues.