Down dog, plank, crow and the forearm balance pincha mayurasana are all much the same pose. The main difference is the angle of the arms relative to the torso and angle of the hips. From my perspective, and current way of practicing, the spine stays much the same--long and free.
In these poses, the abdomen is also made firm. However, it is made firm by the posture not because you are 'sucking in'. In this way of practicing there is no need to actively pull navel to spine and you can breathe into the belly. It won't move too much because it has been made firm by the posture (if performed correctly) but the act of breathing into it will help give you power and relaxation. Please link to Simon Borg Olivier's work on this matter if you are in doubt. Also, watch Paddy McGrath as she practices (you can google them both). You will see how long and free her spine is as she moves between postures like this.
These issues--length and freedom in the spine along with firmness in the abdomen created by the posture--are important things to consider when 'looking' for a feeling in the postures I describe below.
You will see that kneeling plank, when performed as described, is the foundation for all of the poses.
You will see also that kneeling plank, when performed as described, is a fairly difficult pose.
If you can manage a great kneeling plank, as described, then you will create firmness in your abdomen without needing to pull your belly in. The type of firmness that is combined with ease and will enable you to gracefully come into more challenging poses rather than rely on brute force.
You will cultivate strength, stability and openness around the shoulders without needing to lift weights.
You will find length and freedom in your spine without over mobilizing weak parts.
Here is how. Before you begin, revise my previous posts on using the hands as I will only highlight the main points. Remember do not try anything that might make you uncomfortable. Move mindfully and back off if there is any discomfort. This is a way to come into these poses. I like them because they make me feel firm but free, strong, but relaxed. There are other ways. Find what works for you.
***note that the 'ambient' noise in the background is because I didn't figure out how to get rid of the noise of the person boxing in the gym where I filmed this!
Come onto the hands and knees. Middle fingers point straight ahead, hands a little wider than shoulders. Claw the fingers as though making a fist. Squash the wrists towards one another, roll the underside of your arms towards your face. Elbows straight but not rigidly so.
Knees slightly behind hips.
Breathe into the belly. Let it bloat out like a baby's belly. You will keep breathing into the belly throughout.
Scoop the sitting bones down and forward as though they are moving towards the wrists. Lift the top of the pelvis towards the ceiling. The lower back should lengthen and now the belly will firm without you needing to think of actively tensing it.
Breathe into the belly.
Child's Pose (Balasana)
Beware the tendency to just sag back and let the chest and lower back give way to gravity. The chest still floats up, the sitting bones move towards the wrists.
Press the armpits in the direction they face--now towards the floor.
Feel as though you are pulling your knees towards your wrists.
Push the ribs and chest up towards the ceiling. The upper back will broaden. Push the arms down into the floor to enhance this.
Lightly move the armpits in the direction they face--back towards the knees.
Relax the face and neck.
Breathe into the belly.
From kneeling plank you can move to balasana by shifting the whole torso and pelvis backwards towards the heels. You don't have to sit on the heels.
Downward Facing Dog (Adho Mukha Svanasana)
Keep the actions you have been cultivating in kneeling plank and then child's pose. The only thing that changes now is that the heels start to press backwards, as though to the floor. They might not reach the floor. Who cares? It is not that important. The legs might not straighten. Who cares? It is not important.
What is important is that the foundation you have set--ribs floating up with lower back long--is maintained.
To ensure you can do this, move slowly. If you find yourself starting to sag in your spine then pause. Back off until you are not sagging. Stay there and be content with where you are. Let's use this pose to free and lengthen the spine rather than worry about straightening the legs.
Many people, if not mindful, will push their ribs through towards the floor. Perhaps because a lot of people are photographed doing it and because it feels more stretchy. I am not saying it is bad to feel stretchy. However, the action of pushing the chest through rather than lifting it up will teach you nothing about the more advanced arm balance poses.
Bakasana is basically a variation of kneeling plank but with the knees on the arms. The actions of pushing sitting bones to heels, pushing chest upwards, pulling the knees into the chest, and pressing the armpits in the direction in which they face.
The main difference is that the knees actually move towards the chest rather then just feeling as though they are.
Lift up on tiptoes, place the knees on the upper arms, keep trying to pull the knees up higher, push the sitting bones towards the heels, armpits to waist, chest to sky.
You will feel when. You are ready as you will be able to shift your weight forwards and float up.
Forearm Stand (Pincha Mayurasana)
From down dog, lower to your allows, again without letting the chest or lower back sag. Sitting bones to heels, top of the pelvis back, ribs float towards spine. Head hangs down. You should be able to see your navel. If you ribs poke out or drop you will not be able to do this.
This pose is really tough. Most of us just need to be content to stay here on our elbows for a while, navel gazing. The most common things that happen here are that the chest sags, elbows splay, and shoulders start to drop into ears.
If these things start to happen then try to rectify them and, if you cannot, go back to kneeling plank and down dog, every now and then coming back to Pincha Mayurasana to see if you can maintain the position without losing the foundations you have set.
The lower back is lengthened by moving the sitting bones down and forward towards the wrists, top of pelvis up to the sky.
The middle and upper back are lengthened as the ribs and chest move back towards the spine or ceiling.
The armpits press in the direction they face.
The posture creates firmness in the belly. Don't try to pull it in. Breathe into the belly.
Relax the neck and face.
Remember, move slowly. If anything does not feel good, back off or don't do it.
May your practice be safe, peaceful, and happy.