Learn Italian: Non è la medesima sfumatura di viola. - It is not the same shade of purple.

Yes, absolutely. medesima and stessa are perfectly interchangeable when used before the noun to mean "the same" (indicating exact identity). medesima is just slightly more formal or elevated in tone.

If I wanted to emphasize "the shade itself", where would medesima go?

You would place it directly after the noun: la sfumatura medesima. When placed before the noun, it means "the same [noun]", but when placed after, it acts as an intensifier meaning "[noun] itself".

Why is it sfumatura di viola (noun + preposition + noun) instead of just using viola as an adjective (sfumatura viola)?

Both are actually correct! You can treat viola as an invariable adjective and say la medesima sfumatura viola. However, phrasing it as a noun with di ("shade of purple") is very natural in Italian, just as it is in English.

Does the word sfumatura have anything to do with smoke (fumo)?

It does! It comes from the verb sfumare (to fade, blend, or evaporate away like smoke). In the context of colors, a sfumatura is a subtle shade or nuance, referring to how one color might gradually blend into another.