1.yeah,normally both of them mean "especially"
2."经营" means "manage"or"organize"or even"administrate",it's a verb
while "经理" means "manager",it's a noun.
meanwhile,"经理" could also be a verb which means "manage",but just few times.
3.usually "落" means someTHING fall down from top,but "摔倒" means someONE fall down while walking