Deciding whether a Language is Context-free/Regular/Non Context-Free
Your reasoning for the positive statements seems sound to me, although they lack some detail if formal proofs are required. In particular, you might at least want to give the automata for $L_4,L_5,L_6$ and $L_7$; especially the latter can be considered non-trivial, depending on your level of expertise.

You lack proofs for


$L_2 \notin \mathrm{REG}$ and
$L_3 \notin \mathrm{CFL}$.


Both are true and straight-forward to prove; you find all you need in our reference questions for the regular and context-free case, respectively.