Which intermediate is formed when $HCl$ is added to propene in the presence of peroxide?

$A$ compound $X$ absorbs $2$ moles of hydrogen and $X$ upon oxidation with $KMnO_4 \mid H^{+}$ gives the products shown below:
$CH_3-CO-CH_3$,$CH_3-COOH$ and $CH_3-CO-CH_2-CH_2-COOH$.
The total number of $\sigma$ bonds present in the compound $X$ is . . . . . .

The product$(s)$ in the following sequence of reactions will be: $Me-C \equiv C-Me \xrightarrow[2. \text{dil. alkaline } KMnO_4]{1. Na/NH_3(liq.), \text{ethanol}, -33^\circ C}$ Product$(s)$

The reaction of the compound $(CH_3)_2C = CH-CH_3$ with $NaIO_4$ in the presence of $KMnO_4$ yields:

The major product $(P)$ formed in the below reaction is:
$CH_2$ attached to a cyclohexane ring $\xrightarrow[(ii) NaBH_4, OH^-]{(i) Hg(OAc)_2, H_2O-THF} P?$

$CH_3-CH=CH_2 \xrightarrow{HBr} \text{Major product } (A). \text{ } A \text{ is:}$