Everyone here is on the right track. In canon when unfolded, open, and covering something (to what degree the item must be covered is unknown) both the cloak and all covered items and people are rendered invisible.

If the user were to stick her leg out from under the cloak to kick something would onlookers see a completely solid segment of leg floating in midair? Seeing it from behind would they bear witness to a living, moving cross-section of a disembodied leg?

I think, yes, though there is no direct canon evidence. My reasoning is that magic and magical items don't have intelligence. They follow simple formulas (akin to Occam's Razor) to figure out their effects, but have no intelligence to make decisions about what to make invisible or not. Very few magical items in the Harry Potter universe have intelligence (though certainly wands and maybe the sorting hat are exceptions).

Everyone here is on the right track. In canon when unfolded, open, and covering something (to what degree the item must be covered is unknown) both the cloak and all covered items and people are rendered invisible.

If the user were to stick her leg out from under the cloak to kick something would onlookers see a completely solid segment of leg floating in midair? Seeing it from behind would they bear witness to a living, moving cross-section of a disembodied leg?

I think, yes, though there is no direct canon evidence (that I can remember). My reasoning is that magic and magical items don't have intelligence. They follow simple formulas (akin to Occam's Razor) to figure out their effects, but have no intelligence to make decisions about what to make invisible or not. Very few magical items in the Harry Potter universe have intelligence (though certainly wands and maybe the sorting hat are exceptions).