a good phrasing for general description and understanding would be 'grid spacing (levels)'. A bit more special is 'cell size (levels)' as only applicable to cell grids (thus ok for DGGS) but not node grids (often coverages).

I would simply say something like this:

level : int
    Grid hierarchical level. A higher value corresponds to a finer grid resolution
    with smaller cell areas. The number of cells covering the whole sphere usually
    grows exponentially (*) with increasing level values, ranging from 5-100 cells
    (level 0) to millions or billions of cells (level 10+).

(*) or as a power function?

I'd probably try to fit "depending on the specific grid" somewhere in the second sentence, but that's already really great (and as far as I can tell, exponential seems right because we're talking about $n^{\mathrm{level}}$, i.e. the base is constant but the power varies)

I'd have been nice to return from a DGGSInfo instance a cell statistics table like those ones: H3, S2. But I don't think that the core libraries provide such thing via their API, unfortunately.

That could indeed be helpful.

For healpy there's hp.nside2npix, which in any case is 12 * 4**level. As far as statistics like min/max/average area and min/max edge length go, this might be trickier but should not be impossible.

I'd say let's open a separate issue to discuss adding a method like that to DGGSInfo.

Did you consider asking the DGGS API experts?

assuming this is fine (we did have extensive discussion elsewhere), I'm going to merge this tomorrow.

merging. We can always improve later, should it become necessary.