Edit the sketch and look for white dots instead of black dots at the vertices. These indicate open vectors. Zoom in on the area and try to drag the white dot to the intended connection point (nearest black dot). That should close it.
If that doesn’t work, you may have an issue with the vertex being on a different Z level.
Just for learning sake, we would be happy to give the first image a thorough look and see if it was an easy fix. Just share your f3d file. A number of us could take a look and see if it is something simple (usually is). Plus it keeps me off Amazon website if I have something to distract me.
I would say the H is fine, that’s got to be a feature of the handwriting font. As for the other one, the a to r,l my guess would not be related to the slats. It’s probably another factor of the handwritten font. Depending on the source of the font the nodes aren’t always great when converted to cut and they don’t always connect well. Most weren’t meant to be huge and cut out of metal.
You’ve got a good attention to detail though. Lots of people would let that slide (not me) but it’s hard to hit that level of perfection on a $60 sign with a custom modified font.
I would say to use a sander rather than an angle grinder with a flap disc for your top clean up. Or switch to a grinder with a wire wheel. Those grinder scratch marks are distracting.