What is the major product of the following reaction?

One mole of $2-$methylbuta$-1, 3-$diene on ozonolysis gives:

In hydroboration-oxidation reaction $:-$
$I$. Syn addition takes place
$II$. Reaction proceeds through the formation of a cyclic transition state
$III$. Vicinal diol is obtained as a product
$IV$. Anti-addition takes place and Anti-Markovnikov rule is followed
Which of the following statement$(s)$ is/are correct $:-$

$CH_3-CH=CH_2$ $\xrightarrow{Br_2, hv (\text{low conc.})} \dots$ $\xrightarrow{Mg, \text{Dry ether}} \dots$ $\xrightarrow{CH_3-CO-CH_3, NH_4Cl} \dots$ $\xrightarrow{H^{+}, \Delta} (X)$. The end product $(X)$ of the above reaction is:

The product $(P)$ of the following reaction is:

Decolourization of alkaline $KMnO_4$ is used as a test for