The correct order of acidity for the following compounds is:

Product $A$ is

Identify the product $A$ in the following reaction:
(Image of a tricyclic allylic alcohol reacting with $p$-benzoquinone in the presence of $[(CH_3)_3CO]_3Al$ to form $A$)

Which of the following reactions produce carboxylic acids?
$(a)$ $MnO_2$ with $CH_3COCH_3$
$(b)$ $Ph-CCl_3 \xrightarrow[(ii) H_2O/H^+]{(i) aq. NaOH} PhCOOH$
$(c)$ $C_2H_5Br \xrightarrow[(iii) H_2O/H^+]{(i) Mg, (ii) CO_2} C_2H_5COOH$
$(d)$ $CH_3CH=CHCH_3 \xrightarrow[\Delta]{K_2Cr_2O_7/H_2SO_4} 2CH_3COOH$

Considering the reaction sequence given below,the correct statement$(s)$ is(are):
$A$. $P$ can be reduced to a primary alcohol using $NaBH_4$.
$B$. Treating $P$ with conc. $NH_4OH$ solution followed by acidification gives $Q$.
$C$. Treating $Q$ with a solution of $NaNO_2$ in aq. $HCl$ liberates $N_2$.
$D$. $P$ is more acidic than $CH_3CH_2COOH$.

Which of the following is the correct order of decarboxylation of $\beta$-keto carboxylate anion?