How and when is a $\pi$-bond formed by the overlapping of orbitals?

How many $\sigma$ and $\pi$ bonds are present in each of the following molecules?
$(a)$ $HC \equiv C-CH=CH-CH_3$
$(b)$ $CH_2=C=CH-CH_3$

$A$ carbon-carbon triple bond in ethyne $(HC \equiv CH)$ consists of:

$A$ molecule $(X)$ has $(i)$ four sigma bonds formed by the overlap of $sp^2$ and $s$ orbitals,(ii) one sigma bond formed by $sp^2$ and $sp^2$ orbitals,and (iii) one $\pi$ bond formed by $p_z$ and $p_z$ orbitals. Which of the following is $X$?

Match the orbital overlap figures shown in List-$I$ with the description given in List-$II$ and select the correct answer using the code given below the lists.
List-$I$:
$P$. Two $d$-orbitals overlapping axially with same phase.
$Q$. $A$ $p$-orbital and a $d$-orbital overlapping laterally with same phase.
$R$. $A$ $p$-orbital and a $d$-orbital overlapping laterally with opposite phase.
$S$. Two $d$-orbitals overlapping axially with opposite phase.
List-$II$:
$1$. $p-d$ $\pi$ antibonding
$2$. $d-d$ $\sigma$ bonding
$3$. $p-d$ $\pi$ bonding
$4$. $d-d$ $\sigma$ antibonding
Codes: $P \quad Q \quad R \quad S$

Determine the number of $\sigma$ and $\pi$ bonds in the following molecules:
$(i)$ $O_2$
$(ii)$ $N_2$
$(iii)$ $C_6H_6$ (Benzene)
$(iv)$ $O_3$ (Ozone)