Yes. Unless the fonts contain old style superior/inferior figures (I don't know of any besides one of mine, but there sure are), go with the ones included in the font. These are better than scaling a set of old style figures to fit, because the weight will be all wrong. For the listing, lining figures are useful for marking the hierarchy: the listing numbers lining, the numbers in the notes old style.

Yes and yes. Then, as always, you should look how well they work in your setting, and fine-tune your style accordingly.
As an example, in one layout I did using Chaparral as text font, I used the less proper numerator Open Type option because it sits lower and I had a pretty tight leading. Also, I bumped up a bit its size.

If you’re not using a size-specific (a.k.a “optically scaled” or “micro”) font for the footnotes, I would suggest that the numbers in the footnotes be full size, rather than superscript. Otherwise they may be too slight.

But really, if you’re going to the trouble of using proper superscript reference numbers, you should also be using a size-specific font for the footnotes themselves.

With Cala, which has no “opticals” per se, you could use Light for the main text, and Regular for the footnotes, with relative sizing &c. that produces the effect of similar weight.

Brilliant, thanks all for the – as ever – very helpful replies.

I would second the recommendation not to put the figures in the footnotes themselves in superscript: it's what you're looking for at the bottom of the page, so there's really no point in making them small. If you have the space, another nice detail is to have the footnote text indented slightly, as they do here (although they unfortunately superscript the reference in the footnote itself).