The relevence of whether it is captured in a screenshot is that it gives a clue as to whereabout in the driver it fails - or rather it rules out several potential candidates. A GPU hang will indeed be first noticed by a stutter and be recorded in the kernel log - on your system, it should not require a reboot except in exceptional circumstances.
Not sure about the libreoffice glitch, that I would say is more likely to be a gui issue rather than driver, but you already have too many weirds things happening that one more wouldn't surprise me.
The relevence of whether it is captured in a screenshot is that it gives a clue as to whereabout in the driver it fails - or rather it rules out several potential candidates. A GPU hang will indeed be first noticed by a stutter and be recorded in the kernel log - on your system, it should not require a reboot except in exceptional circumstances.
Not sure about the libreoffice glitch, that I would say is more likely to be a gui issue rather than driver, but you already have too many weirds things happening that one more wouldn't surprise me.