Is WWE fighting real

Yes and no. Some certain moves--such as punches and similar moves (back chops, some forms of kicks, etc.)--are fake. However, some moves cannot be faked, such as most moves involving picking up the opponent (scoop slam, powerbomb, chokeslam, Samoan drop, fireman's carry, etc.) and diving moves.

Injury wise, some are real. For example, if a wrestler leaves for a long time due to an injury, it is most likely real. But if a wrestler is injured in an unusual way, or it is shown on the show (often in a way that it doesn't seem real), it is fake. For example, WWE superstar The Big Show once got ran over by a car. Something like this would most likely not be video taped and shown on TV; however it was. This injury was fake. Most injuries that cause wrestlers to leave for a certain period of time (usually anywhere between about 1 month or 1 year) are real.