It took me a few seconds to see that you do have the breaths included - the IN and OUT and IN + OUT in the posture with the eight points of contact - "Butt up."
They are good drawings. The Cobra can be and often is done alternatively with the Swan (Hamsasana). The difference is that in the Cobra the arch is from the head to the solar plexus. And in the Swan the arch is all the way down to your hips. If you imagine straightening the arms from the position as shown in the Cobra picture (which is correct) - it puts you in the Swan.
Breathing is through the nose, of course, with the exception of a "cleansing breath" before bringing the palms together in namasté at the beginning which is done expelling the dead air from your lungs through the mouth with a little friction in the pharynx as you expell the air. When you draw the breath in - and all the way through the twelve postures you should breathe comfortably through your nose.
And if you like to hang in the forward bends for a while it's perfectly acceptable to take shallow breaths after the outbreath that gets you down there. It will help particularly at the end of a period of hanging and relaxing, to go up smoothly either caterpillar style keeping your face close to your legs as you start; or you can come up "flat backed" moving your head away from your legs.
Beginners should do it caterpillar style; and even advanced yogis should make sure they are warmed up before doing any of the very strenuous postures including the variotions in the sun salutation. There are a few postures that are strenuous.
The Locust would be one of those; perhaps the most intense other than Baby Krishna pose and a few others most of us will only see in books or at the circus.
The sun salutation is a good thing to come back to if you are an advanced yogi.
And you can embellish it too - with a few extra movements - like going from namasté in the lunges to "arms back"in a graceful sweeping of wing type movement with an inbreath between the moves watching your fingertips as you move into the respective postures that follow. You have to return of course - in order to come to the floor or to come back to hanging in the second forward bend.
It is rewarding to get the breaths smooth and corresponding with the motions.
Don't forget to lie flat on your back when you're done in savangasana (corpse pose) keep breathing and relax before you get to the next posture, a medition period, or the rest of your day.