To answer this question, we need to calculate the number of Faraday's required for each of the reactions in List I.

Reaction A: Conversion of H₂O to O₂

The reaction for electrolysis of water to produce oxygen can be written as:

$$\text{2H}_2\text{O (l)} \rightarrow \text{O}_2\text{(g)} + 4\text{H}^+ + 4\text{e}^-$$

Each mole of O₂ requires the transfer of 4 moles of electrons. Therefore, to produce 1 mole of O₂, you need 4 Faraday's of charge. However, since the reaction shown in the table suggests the production of only 1 mole, it would require 2 Faraday's. This is because we are dealing with a half reaction in which only 2 moles of electrons are required for every mole of O₂ produced from 1 mole of H₂O.

Reaction B: Conversion of MnO₄^- to Mn²⁺

The reduction reaction for permanganate to manganese ion is:

$$\text{MnO}_4^- + 8\text{H}^+ + 5\text{e}^- \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O}$$

This reaction indicates that 5 moles of electrons are involved in the reduction of 1 mole of MnO₄^- to Mn²⁺. Therefore, 5 Faraday's are required.

Reaction C: Production of 1.5 moles of Ca from molten CaCl₂

The electrolytic production of calcium from its chloride can be illustrated as follows:

$$\text{Ca}^{2+} + 2\text{e}^- \rightarrow \text{Ca}$$

Each mole of Ca produced requires 2 Faraday's of electrons considering the transfer of 2 moles of electrons. For 1.5 moles of Ca, the total Faraday's required would be 3 Faraday's, because, 1.5 * 2 = 3F.

Reaction D: Oxidation of FeO to Fe₂O₃

The reaction can be considered in terms of iron oxidation states:

$$\text{4FeO} \rightarrow \text{2Fe}_2\text{O}_3 + \text{O}_2 + 4\text{e}^-$$

Each mole of O₂ requires 2 Faraday's of charge. If the products include 2 moles of Fe₂O₃ and 1 mole of O₂, thus, only 2 Faraday's will be required for 1 mole of FeO to react (considering FeO as just a part of the full reaction).

Correct Matching:

A-II, B-IV, C-I, D-III

The mappings are A-II (2F for H₂O to O₂), B-IV (5F for MnO₄^- to Mn²⁺), C-I (3F for 1.5 mol of Ca from CaCl₂), and D-III (2F for FeO to Fe₂O₃).

Therefore, the correct answer is Option A:

A-II, B-IV, C-I, D-III.