Hydrocarbons: describe question

A chemist investigates an unknown alkene, X, with the molecular formula $\ce{C4H8}$. Treatment of X with hot concentrated acidified $\ce{KMnO4}$ yields a single carboxylic acid. When X is reacted with $\ce{HBr}$, a single product is formed. Subsequent treatment of this product with ethanolic $\ce{NaOH}$ and heat produces a different alkene, Y.

(a) Describe the reaction of X with hot concentrated acidified $\ce{KMnO4}$, stating the type of reaction and the identity of the carboxylic acid formed.

(b) State the reagents and conditions for the conversion of X into Y via the two-step process described. Write equations for both steps, using structural formulae.

(c) Describe the addition polymerisation of propene, including the type of polymerisation and the structure of the polymer.