Even though for CO₂ and CH₄ the C - O and C - H bonds are polar but due to their symmetrical structure they have zero dipole moment.
In NH₃, H is less electronegative than N and hence the dipole moment of each N-H bond is towards N which is in the similar direction of lone pair but for NF₃ the dipole moment of N-F bond is in opposite direction of lone pair which reduce the value of net dipole moment.

Water is a polar compound so the salt which is more polar or having more ionic character will be more soluble in it. According to Fajan's rule, ionic character of compound increases with increase in the size of cation. Now, among the given compounds, the size of cations are in the order as follows :

Na⁺ > Zn²⁺ > Cu²⁺

Thus, the order of ionic character and the solubility order in aqueous medium is as follows :

Na₂S > ZnS > CuS

Molecular orbital configuration of

O₂⁺ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\sigma 2p_z^2\pi 2p_y^2{\pi ^*}2p_x^1{\pi ^*}2p_y^1$$ $$ \Rightarrow $$ Paramagnetic

Bond order = $${{10 - 5} \over 2} = 2.5$$

C₂ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\sigma 2p_z^2\pi 2p_y^2$$ $$ \Rightarrow $$ Diamagnetic

Bond order = $${{8 - 4} \over 2} = 2$$

C₂⁺ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\sigma 2p_z^2\pi 2p_y^1$$ $$ \Rightarrow $$ Paramagnetic

Bond order = $${{7 - 4} \over 2} = 1.5$$

NO $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\sigma 2p_z^2\pi 2p_y^2{\pi ^*}2p_x^1$$ $$ \Rightarrow $$ Paramagnetic

Bond order = $${{10 - 5} \over 2} = 2.5$$

NO⁺ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\sigma 2p_z^2\pi 2p_x^2\pi 2p_y^2$$ $$ \Rightarrow $$ Diamagnetic

Bond order = $${{10 - 4} \over 2} = 3$$

N₂ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\pi 2p_x^2\pi 2p_y^2\sigma 2p_z^2$$ $$ \Rightarrow $$ Paramagnetic

Bond order = $${{10 - 4} \over 2} = 3$$

N₂⁺ $$ \Rightarrow $$ $$\sigma 1{s^2}{\sigma ^*}1{s^2}\sigma 2{s^2}{\sigma ^*}2{s^2}\pi 2p_x^2\pi 2p_y^2\sigma 2p_z^1$$ $$ \Rightarrow $$ Paramagnetic

Bond order = $${{9 - 4} \over 2} = 2.5$$