Carcassone scoring for a city with a mayor and a cathedral
The Mayor doesn't affect the number of points received for completing a City.  The Mayor only affects WHO might get the points.  If someone has a meeple in a city and you get your Mayor in the city, the mayor counts as the number of pennants in that city. 

So if the City had 0 pennants, then your mayor would be 0 and the other meeple would be 1, allowing them to have 'more' meeple.  If there was 1 pennant, then you would tie and both get the score.  If there were 2 or more pennants, than you would have more meeple (the number of pennants) and would 'win' and get all the points your opponent getting nothing.  

The Cathedrals as you've noticed changed values from 2 points/tile and pennant to 3 per.  So a city with 8 tiles and 2 pennants would go from 20 points to 30 points.  Who ever has the most meeple in the city gets all the points (tie both get the same)