What are $X$ and $Y$ in the following set of reactions?

When ethyl acetoacetate reacts with one mole of methyl magnesium iodide,the product of the reaction will be:

The increasing order of the reactivity of the following compounds with $LiAlH_4$ is:
$(a)$ $C_2H_5CONH_2$
$(b)$ $C_2H_5COOCH_3$
$(c)$ $C_2H_5COCl$
$(d)$ $(C_2H_5CO)_2O$

The vapour of a carboxylic acid $HA$ when passed over $MnO_2$ at $573 \ K$ yields propanone. The acid $HA$ is

When carboxylic acid reacts with organolithium reagents to give ketones,side reactions sometimes occur. For example,
$HOCH_2CH_2CH(CH_3)CH_2CH_2COOH$ $\xrightarrow[(x) \, CH_3Li]{tetrahydro\,furan}$ $\xrightarrow[NH_4Cl]{H_2O}$ $\underset{63\%}{\text{Compound } A: HOCH_2CH_2CH(CH_3)CH_2CH_2COCH_3}$ + $\underset{37\%}{\text{Compound } (B)}$
The value of $(x)$ in the above reaction is:

The product of the reaction will be :