Can the amortized cost be negative? That is to say, can $c_i + \Phi(D_i) - \Phi(D_{i-1})$ be negative?

Yes, it is possible.

The reduction in the potential might be larger than the actual cost of the operation.

As you said, we found out that it's negative, but on page 86 at "Abstract data types, stack, queue, amortized analysis" presentation, the conclusion at the bottom line is amortz>= 2. So why is that?

This line explains the following.

One might think that since the amortized cost of a pop operation is negative we might gain credit (i.e. we might have a negative potential) by repeatably preforming pop operations.

However this is not true, since the number of pop operations is limited by the number of push operation, and so the potential is always positive.

What this means is that the amortized cost of a single operation might be negative, but the amortized cost of a sequence of operations will always be non-negative (assuming the initial potential is 0).