>>13242322First of all red blood cells are a bad example because they are a simplified version of a cell. They are produced without a nucleus so they have room to carry oxygen and other nutrients throughout the system. The circulatory system is also a closed loop so they don't interact with or have access to the outside world a whole lot, and they have short lives and no "brain" (nucleus) to direct their actions.
They don't battle because they all have the same DNA, and antigens on their outside surfaces that all identify to each other as "self". There is no reason to fight yourself. Multicellularism evolved out of clumps of single-celled organisms that exchange nutrients which form mutually beneficial relationships. Nature isn't red in tooth-and-claw, there are symbiotic relationships that form all the time, and this happens on a cellular level as well. Multicellular organisms are the result of millions of years of evolution adding complexity to these relationships.
They synchronize their actions using primarily chemical signals of complex molecules. They use chemicals/structures such as hormones or enzymes to create complex chemical chain reactions in order to respond to their environments.