Monster shouldn't disappear if I lost a battle
I think it would be a good idea, if a monster would not disappear after I lost the battle against it. First this would be more "realistic" because it's not dead and, well, still staying here. Second this would offer the opportunity to try different strategies to beat it.
I definitely agree with you here.
Not a good idea, as it will be to easy to death train skills. Pick 1 spell from each type find a mob you know you can easily last against the get you +15 skill in each group and then let it kill you, rinse and repeat.
I agree with @Antony-Hollinsworth and the idea only pro is making it more "realistic". Finding another monster is not that hard and if you want realism you should ask for death penalties first
I think you're absolutely right - I didn't consider this aspect.