Accessible palette generator
Nearest named colour: gray
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Generates a muted palette: the range most likely to give usable contrast, and points you at the contrast checker, because no generator can guarantee an accessible pair.
How to use the accessible palette generator
It is worth being straight about what "accessible palette generator" can mean. A generator can bias toward a range where good contrast is likely, which is what this does by favouring middling lightness and low saturation. It cannot certify a palette, because accessibility is a property of pairs in context; this text on that background at that size, not of a set of colours. A five-colour palette has ten possible pairs and most of them will fail; the useful workflow is to generate, pick your text and background, and check that specific pair.
Questions
No. Accessibility is a property of a text-and-background pair at a given size, not of a colour set. Generate, then check your pairs.
Middling lightness and low saturation is the range where usable contrast is most likely in both directions.
Only the ones you will actually use. A five-colour palette has ten pairs and most are irrelevant.
4.5:1 for body text, 3:1 for large text and interface components.
Hex for anything going into a design tool, HSL when you want to adjust lightness by hand, and OKLCH when you need two colours to look equally light; it is the only one of the four where that number means what you expect.