The reaction of sodium acetate with acetyl chloride proceeds through which of the following mechanisms?

The product is:

The following transformation can be carried out in three steps. The reagents required for these three steps in their correct order are:

The product $(C)$ of the above reaction is:

With reference to the scheme given,which of the given statement$(s)$ about $T$,$U$,$V$ and $W$ is (are) correct?
$A$. $T$ is soluble in hot aqueous $NaOH$
$B$. $U$ is optically active
$C$. Molecular formula of $W$ is $C_{10}H_{18}O_4$
$D$. $V$ gives effervescence on treatment with aqueous $NaHCO_3$

The conversion of $CH_{3}CH_{2}COOH$ to the product shown below can be accomplished by:
$CH_{3}CH_{2}CH(OCH_{2}CH_{2}O)$