Here the given language is $\phi$ which is empty set {} .
So , L={}=$\phi$
now , we know by definition for any language $L^{0}=\left \{ \epsilon \right \}$
$L^{1}=\left \{ \right \}=\phi$
$L^{2}=L.L=\left \{ \right \}\left \{ \right \}=\left \{ \right \}=\phi$
$L^{3}=L.L.L=\left \{ \right \}\left \{ \right \}\left \{ \right \}=\left \{ \right \}=\phi$
So ,
$\phi^{*}=L^{*}= L^{0} \cup L^{1} \cup L^{2} \cup L^{3} \cup L^{4} \cup L^{5}\cup…………. $
$\phi^{*}= \left \{ \epsilon \right \} \cup \left \{ \right \}\cup\left \{ \right \}\cup\left \{ \right \}\cup………...$
$\phi^{*}=\left \{ \epsilon \right \}$
$\phi^{+}=L^{1} \cup L^{2} \cup L^{3} \cup L^{4} \cup L^{5}\cup…………. $
$\phi^{+}$ =$\left \{ \right \}\cup\left \{ \right \}\cup\left \{ \right \}\cup………...$
$\phi^{+}$=$\left \{ \right \}$
For 3rd I think the question wrong as $\phi$ is a set and $\epsilon$ is a string . So how can we define an Cartesian product of a set an a string ? Moreover Cartesian product term is wrong for language concatenation as Cartesian product will give us ordered pair not a language.
More details explained in the Link.