In the titration of $I_{2(aq)}$ by $S_2O_3^{2-}{_{\text{(aq)}}}$ using the starch indicator, the end point is indicated by:

$0.4 \ g$ 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)

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:

$3.92 \, g$ of ferrous ammonium sulfate crystals are dissolved in $100 \, mL$ of water. During titration,$20 \, mL$ of this solution is required for complete oxidation by $18 \, mL$ of $KMnO_4$ solution. Calculate the weight of $KMnO_4$ in $1 \, L$ of the solution in grams.

$10.0 \, mL$ of $0.05 \, M \, KMnO_4$ solution was consumed in a titration with $10.0 \, mL$ of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is $..... \times 10^{-2} \, g / L$ (Round off to the nearest integer).

Can titrations with $KMnO_4$ be performed in the presence of $HCl$? Why?