Neural Network - Adjust number of hidden layers and neurons
Sorry for not knowing exact number for the first question, but my point is to start from the most simple model, rather than any random parameter. Then use a grid search for the parameter by validation. 

As for the second question, the error of a model comes from two parts, variance and bias. Bias comes from lack of complexity of your model. For example, there will always be a large bias when using linear model to fit the distance v.s. the shooting angle of a canon. This can be overcome by using a more complex model,  adding layers to the NN for example. 

And variances comes from being too sensitive to the data, even to the noise in the data. When there is a high variance due to using a too complex model, it is called over-fitting. You may take a look at this page(over-fitting on wiki). And using more layers/neurons is using a more complex model, which means the model may suffer from high variance. This can be overcome by lower the model complexity(which may increase the bias) or adding training data.

Basically if you got constant number of data, then you have to find somewhere where both bias and variance is not too high.