Building non-deterministic automata
I have tried this question to the best of my ability. Feel free to ask for any clarification or raise any doubts in the comments.

Apart from issues like nullifying the effect of some useful transitions, the problem in your solution is that you've started out at a rejecting state, but unless the string has encountered $bb$ and then $cba$ and subsequently $cc$, it should be accepted.
I've laid out the transitions in a step wise manner, jumping about the states to &quot;reset&quot; the logic that proceeds to rejecting state.
Update:
You can think about the automata as comprising of $3$ parts. q0,q1 check for first occurrence of $bb$. q2,q3,q4 detect the string $cba$. Finally, q5,q6,q7 test for the string $cc$.