Keras Loss Function for Multidimensional Regression Problem
To answer:

1) When calculating the loss function for multivariate outputs, keras calculates it as a mean across all your outputs: https://github.com/keras-team/keras/blob/2.0.4/keras/losses.py#L12

Hence, if one output is doing really badly and others not, it could influence your loss result.

2) In the source code there are no mentioning about scaling the outputs for the calculation of loss function and, thus, I would conclude that the loss function will depend highly on the boundaries of each of your Y features.

To avoid this, what you could do is to write a custom loss function that scales your Y outputs before outputting loss value:

scaler = MinMaxScaler()
data_trans = scaler.fit_transform(y_true)

def custom_mean_absolute_error(y_true, y_pred):
    y_true = (y_true - K.constant(scaler.min_)) / K.constant(scaler.scale_)
    y_pred = (y_pred - K.constant(scaler.min_)) / K.constant(scaler.scale_)
    return K.mean(K.abs(y_pred - y_true), axis=-1)