1. One problem could be that we haven't normalized our training inputs. Another could be that the training rate was too large.
2. With a small training rate a set of weights might converge very slowly, or not at all.
3. A large training rate can lead to a set of weights being over-fit to particular batch values or this training set. Also, it can lead to numerical overflows/underflows as in the first problem.
4. Sigmoid.
5. Softmax.
6. More updates.