Solution: Shapes
Answer: DIAMOND BROOCH

Written by Jonathan

This is a mangled clues puzzle. The answer for each clue makes a phrase with a shape.

Clue Transformation Clue answer Reapply transformation Phrase with Shape
European country hosting Olympics this year (5) Drop first letter change second letter to D FRANCE DANCE SQUARE DANCE
Gentle wind or something that is easy to do (6) Change 1st letter to F BREEZE FREEZE FREEZE FRAME
File container for papers (6) Change 1st letter to G, last letter to N FOLDER GOLDEN GOLDEN RECTANGLE
Daily period of darkness (5) Rot +4 to first letter NIGHT RIGHT RIGHT TRIANGLE
Manageable, practical or possible (6) Change second vowel to U DOABLE DOUBLE DOUBLE CROSS
Appetizing food giving exquisite pleasure (9) Drop first 2 letters, change 3rd letter to V DELICIOUS VICIOUS VICIOUS CIRCLE

The last line has all their last vowels changed to O to give the cluephrase INDOX FOOR TWO TWO TWO THREO FOOR.

Shape order in the last row Phrase with Shape Non-shape word Given index Indexed letter
Cross Double cross Double 4 B
Frame Freeze frame Freeze 2 R
Rectangle Golden rectangle Golden 2 O
Square Square dance Dance 2 A
Circle Vicious circle Vicious 3 C
Triangle Right triangle Right 4 H

The indices give us BROACH. Note that the last line had all the last vowel changed to O, and we can reapply this transformation again to get BROOCH. We then prepend a shape again (since there was 1 last transformation) to get the final answer, DIAMOND BROOCH.