What will the following expressions evaluate to? I. (B || C) && (C && a)

We do not do your homework: it is set for a reason. It is there so that you think about what you have been told, and try to understand it. It is also there so that your tutor can identify areas where you are weak, and focus more attention on remedial action.

Try it yourself, you may find it is not as difficult as you think!
Take them one at a time, and break them down into parts. Solve the parts one at a time, and combine them to get each answer.

If you meet a specific problem, then please ask about that and we will do our best to help. But we aren't going to do it all for you!

You should do your homework. If you would liste to your teacher or read your course note, it would not be that hard at least for some cases...

For case (i), you could you could distribute B || C to the rest of the equation and then you can simplify the equation as one part is included in the other.

Case (ii) is very trivial to solve.

Case (iii) is somewhat more difficult but you use rule like !X || !Y is equivalent to !(X && Y) a few times. Alternatively, you can draw a truth table, and find the solution.

A B C   !A   !C   (...)   C   !B   (...)   result
0 0 0    1    1     1     0    1     1        1
0 0 1    1    0     1     0    1     0        1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Case (iv) has some trivial simplification...

You have to do other exercise all by yourself... So later cases seems to be incorrect either as code or mathematical expression. Also, for some of those cases, other information is required...