They look as if the are trying to keep the hive cooled and the use of water helps them to do this, when they evaporate the water in the hive it cools it down, they are outside the hive to allow better ventilation since you installed the entrance reducers.
Have you tried a top hive ventilation? there are several threads that talk about it.
All I did was prop up the top cover on my hives to allow some air flow and not allow the bees an entrance thru the top, that way they can't get robbed thru another entrance and wouldn't need to post guards there.
I live in Arkansas and it get hot here, and since I've done this they haven't been bearding, I noticed when they need to close the entrance down in the evenings they just bunch up in the opening to restrict the ventilation.
As for them fighting this is normal when there isn't a nector flow on and they start to guard from robbing, there are several thousand bees in a colony and everyday some are dying and new ones emerging, a few dead bees is normal I would think, after all any battle has it's casualties.
This is my first year beekeeping also, but, I've been given the advantage of being able to work with a 40 year + beekeeper, I have asked him hundreds of questions, and read on this forum everyday, about every new topic, every new post. It goes with my coffee in the mornings, LOL
This is just my opinions from what I've learned here and in the field