Answer
Statement (iii) is incorrect.
Work Step by Step
Let's go through each statement.
(i) This statement can in fact be represented as follow $$Z_{eff}=Z-S$$
where $Z$ is the nuclear charge of the element and $S$ is the screening constant.
That formula is exactly the formula to calculate $Z_{eff}$. And since effective nuclear charge is the representation of the attraction between the nucleus and electron but is screened by other electrons, that statement is correct.
(ii) As we go from left to right across a row, the nuclear charge $Z$ increases constantly, corresponding to the increasing positive charge of the nucleus as more protons are present.
However, the screening constant $S$ would remain quite unchanged, since though the valence electrons do increase, they do not have much influence on the screening effect.
Therefore, according to the formula $Z_{eff}=Z-S$, $Z_{eff}$ would increase from left to right across a row. That statment is correct.
(iii) As we have said above, the valence electrons do not have much influence on the screening effect to the nuclear charge. Instead, almost all screening effect is produced by the core electrons. So this statement is incorrect.
(iv) At statement (iii), we already argue that most of the screening effect is produced by core electrons. As we move from the end of one row to the beginning of the next row, all the valence electrons would suddenly become core electrons.
As a result, a lot more core electrons are added, which act to screen the nuclear charge effectively. Therefore, the effective nuclear charge would decrease by a huge amount, due to the added screening effect. The statement is correct.
(v) As we go from left to right across a row, the nuclear charge increases quite constantly, while the screening effect does not change much. So, the change in effective nuclear charge quite dramatic.
Instead, as we go down a column, the increase of nuclear charge is challenged by the addition of a great number of core electrons which switch from valence electrons before. Therefore, the change in effective nuclear charge is obviously less dramatic.
The statement is correct.
