You are supposed to breathe in while descending and breathe out while raising. This is according to 7 Weeks to 100 Push-Ups: Strengthen and Sculpt Your Arms, Abs, Chest, Back and Glutes by Training to do 100 Consecutive Push-Ups. Do not hold your breath.
If doing pushups is stressing your wrist, you can hold your hands into fists with knuckles to the floor. But make sure you are on a soft mat or have the hands over soft towels.
On page 39 of the book, the book gives you a table of how many push ups a male or female is supposed to be able to do on average for a given age group. As an example, an average middle-aged male between 40-49 years should be able to do 13 to 21 pushups on average. For females, it would be 7 to 14.
A male over the age of 60 who is able to do more than 28 pushups is considered excellent. 16 or more pushup for females over the age of 60 would be most excellent as well.