Looks to me that because the batteries are dead, they are drawing all your solar power to recharge. Maybe? The reason turning them off and on allows power is that if gives you a hair over what the batteries require to recharge. That hair over remains positive as long as there is sun. Just an idea. Question here: Do you get plague if the lights aren't lit? If you still don't get plague than it's a graphic issue. If you do, than it's a power issue.
As for trees, if you plant it, it requires water. If the RWG placed it, it does not.