1.

n.      A -> (B-> C)
n+1    B
n+2    C                    (n; n+1; MP)

This is wrong because B -> C is not the whole of n.  Think about it.  Step n says "if A, then if B then C"; so, even if B is true, as step n+1 says, we cannot get C unless we also know that A is true.  Suppose that A is "the room is full of gas"; B is "the match is lit"; C is "there's an explosion".  Then, n says "if the room is full of gas, then if the match is lit there is an explosion".  Even if B is true, we cannot infer C unless we know that A is true as well.

2.

n.        -(A v B)
n+1        -A v -B   (n)

The problem here is that n and n+1 have different truth tables (check it out!). n tells us that it's false that either A or B is true (i.e., it tells us that neither A nor B is true).  By contrast, n+1 tells us that one or possibly both of A and B is false.

3.

n.      A -> B
n+1    -A
n+2    -B        (n; n+1)

This is a really big mistake.  If you make it, you should kick yourself because you deserve it.  n says "if A then B"; but, of course, even if A is false, it doesn't follow that B is false.  Compare: "if it snows, then it's cold; it doesn't snow; hence it's not cold".  Snow is a sufficient condition for cold, but lack of sufficient condition doesn't entail lack of necessary condition.  Note that there would be no mistake if n were A <-> B  (WHY?).

4.

n        A -> B
n+1.    B
n+2    A          (n; n+1)

As bad as (3). So, kick yourself again if you make this mistake.  The presence of a necessary condition doesn't entail the presence of a sufficient condition (cold by itself is doesn't get you snow, right?).  Note that there would be no mistake if n+1 were -B and n+2 were -A  (WHY?).

5.

n        -(A -> B)
n+1    -A -> -B    (n)

The mistake here is that n and n+1 don't have the same truth table (check it out!).  For example, suppose that n is "it's false that if it's hot then it snows"; then, one cannot infer that if it's not hot, then  it doesn't snow, right?

6.

n        -(A & B)
n+1    -A & -B    (n)

The mistake here is that n and n+1 have different truth tables (check it out, don't just stare at this!).  n says that it's false that both A and B are true;  n+1 says that neither A nor B are true.  So, they're different, right?