Which reagent is commonly used in titration to determine the hardness of water?

Given below are two statements:
Statement $I$: In the oxalic acid vs $KMnO_4$ (in the presence of dil. $H_2SO_4$) titration,the solution needs to be heated initially to $60^{\circ}C$,but no heating is required in Ferrous Ammonium Sulphate $(\text{FAS})$ vs $KMnO_4$ titration (in the presence of dil. $H_2SO_4$).
Statement $II$: In oxalic acid vs $KMnO_4$ titration,the initial formation of $MnSO_4$ takes place at high temperature,which then acts as a catalyst for the further reaction. In the case of $\text{FAS}$ vs $KMnO_4$,heating oxidizes $Fe^{2+}$ into $Fe^{3+}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements,choose the correct answer from the options given below:

$0.4 \ g$ mixture of $NaOH, Na_{2}CO_{3}$ and some inert impurities was first titrated with $\frac{N}{10} \ HCl$ using phenolphthalein as an indicator,$17.5 \ mL$ of $HCl$ was required at the end point. After this,methyl orange was added and titrated. $1.5 \ mL$ of same $HCl$ was required for the next end point. The weight percentage of $Na_{2}CO_{3}$ in the mixture is .......... (Rounded-off to the nearest integer)

If $25 \ mL$ of $H_2SO_4$ solution is neutralized by $32.63 \ mL$ of $0.164 \ M \ NaOH$ solution,what is the molarity of the $H_2SO_4$ solution?

Temporary hardness in tap water is measured in terms of parts of $CaCO_3$ per $10^6$ parts of water. If $500 \ mL$ of hard water containing $Ca(HCO_3)_2$ was titrated against $\frac{1}{20} \ M \ H_2SO_4$ solution in the presence of a methyl orange indicator,and it required $40 \ mL$ of titrant,then the temporary hardness in the tap water is .............. $ppm$.

$40 \ mL$ of a mixture of $CH_3COOH$ and $HCl$ (aqueous solution) is titrated against $0.1 \ M$ $NaOH$ solution conductometrically. Which of the following statements is correct?