P-NP related 3 sub-problems
You are right about $1$.
For $2$, $L_1$ reduces to $L_2$, means $L_1$ as least as hard as $L_2$. But not vice versa as adding numbers is in $P$ and tower of Hanoi is in $EXP$, so the later is hard but addition does not reduce to tower of Hanoi. Just knowing the hardness does not say much. Hence the statement is false. If it were not the case, then statement $2$ would have been true.
For $L_1, L_2\in NP\;Complete$, as $L_1,L_2\in NP$, $L_1$ reduces to $L_2$ and $L_2$ reduces to $L_1$, according to NP-Complete definition. So, their hardness is same. So, they both belong to the same class. Hence, $L_1\in P\Rightarrow L_2\in P$ and vice versa. So, $3$ is correct.