What other metrics may I use in addition to ‘loss’ or ‘accuracy’ to set up callback rule?
If Im not mistaken - these metrics are also used in model.compile(bla-bla, metrics=[…]) method.
Where do I get more info about it?
There is a lot to use, depending on your choice or nature of the problem. Some of these are MAE, MSE, RMSE, Precision, Recall, etc. Check this list.