Thanks, we have this on the list for refinement. It’s a bit tricky with the algorithm for placing the inspector footnotes, and there’s an option for determining whether it goes inside or outside the punctuation, but some cases of double punctuation like this (period-quote) throw it. Even though there are cases when the footnote marker should appear inside the quotation, if you deliberately put the inline footnote outside the quote, converting it to an inspector note should leave it in the same place, and likewise creating the inspector note after the quotation should place it outside rather than in.
No, the spacing is unrelated. You can though add additional spacing inside the footnote formatting to pad your footnote, so you’re not running your words together. The extra space at the beginning will be stripped out during compile.