Can one chinese character represent many different words?
Yes.

处 also has two different readings:


  chǔ


and


  chù


with many different meanings.

chǔ for instance means:


  to reside / to live / to dwell / to be in / to be situated at / to stay / to get along with / to be in a position of / to deal with / to discipline / to punish 


while chù means:


  place / location / spot / point / office / department / bureau / respect / classifier for locations or items of damage: spot, point 


This is not uncommon, especially with simplified characters as sometimes multiple traditional characters get simplified into the same singular character, you just need to know when what means what.