If we are talking about code placeholders here, then I'm worried that the math font won't harmonize with the teletype font. They have different contrast and different cap height. This may work in certain situations, but it may come to bite us in the future.

I find italic teletype appropriate for the job. Just like "normal" body font italics are appropriate for mathematical variables in the context of body text, italic teletype seems appropriate for "code variables". (Though perhaps we should facilitate disabling the italic correction.)

See also #1060.

Indeed. I think the need for italics in this context is by and large the same as for any code placeholder, so I'd be perfectly happy treating the two the same way.

(Note that for capital letters, the distinction between italic and slanted isn't very big, so either is fine here.)

See #1139 for indexed (type) variables.

We should decide how to proceed and update the wiki accordingly.

Editorial meeting discussion: Variables of different kinds might be formatted differently. Possible kinds: type, variable, object, value, expression. It seems the convention is to use italics for all but the first and last; use code font for those. For meta-variables that expand to code, use code font. For other meta-variables, use math. For string interpolation, use \placeholder. Also for "op" in fold-expression. Update the wiki.
Idea: Introduce \tvar for type placeholders and make them italics. Not pursued.