Can a priest change or leave out parts of the Mass? Where are the rules of how the the Mass should be conducted layed down?
Yes and no. Within Mass there are often several options. Sometimes the priest is allowed to choose which Mass will be said. For the Creed the celebrants can recite either the Nicene or the Apostles Creed. During weekday Masses the Prayer of the Faithful and homilies are optional. However, outside of the handful of legitimate options the priest is not allowed to make any changes to Mass.
Basic information about the Mass can be found in the General Instruction of the Roman Missal.