They're only vaguely related.
Font hinting refers to "hints" about how to rasterize a font to a screen. See
here. The intent is to provide clearer text at the expense of accuracy to the font's actual shape.
The higher the DPI, the less the distinction matters.
As an aside, if you long press on "font hinting" it'll provide you with a little bit of an explanation within the program, although how clear it is in this case is another matter.
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TOC hints are explained in the about alternative TOC menu item. If you're only seeing this through Weblate, if you click through to the code you'll actually see that explanation right next to it:
https://github.com/koreader/koreader....lua#L582-L591 
The general idea is the same as with font hinting. A document will typically include a TOC, but if it doesn't, it'll often still include headers. Those headers can be used as "hints" to build a TOC.
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The last one is a bit different. In this case it's some type of visual hint to the user that a book contains a description. I'm not the biggest fan of what it looks like, but it's also hard to come up with something much better. See the attached screenshot, top without a hint, bottom with a hint.