Find the oxidation state of sodium in $Na_2O_2$.

Given below are two statements.
Statement $I$ : In $H_2O_2$, each oxygen atom is assigned an oxidation number of $-1$, and in $RbO_2$, each oxygen atom is assigned an oxidation number of $-\frac{1}{2}$.
Statement $II$ : The representation of $HAuCl_4$ and $MnO_2$ in Stock notation is $HAu(III)Cl_4$ and $Mn(IV)O_2$ respectively.
Examine the above statements and choose the correct answer.

Write the oxidation number of the carbon atom in the carboxyl group of acetic acid $(CH_3COOH)$.

The oxidation number of $S$ in $H_2S_2O_8$ is

Arrange $ICl$,$HI$,$I_2$,and $HIO_4$ in the decreasing order of the oxidation number of iodine.

Match the following compounds with the oxidation number of the central atom (or specific atom in question):

Compound	Oxidation number
$1$. $C_6H_{12}O_6$ (Carbon)	$a$. $+1$
$2$. $CCl_4$ (Carbon)	$b$. $0$
$3$. $NH_4Cl$ (Nitrogen)	$c$. $+4$
$4$. $Ba(H_2PO_2)_2$ (Phosphorus)	$d$. $-3$