You can crouch in mid air. I don't think there is an animation for walking in the short time it takes from standing to crouching. It would look goofy if it was implemented without making the animation. Your spartans legs wouldn't move in relation to the ground until you were fully crouched and the crouch walking animation started.
Yes, you can walk while crouching, but once you reach a certain speed, you will automatically stand up. Most people never notice because the default controls have crouch and move on the same stick. It’s more obvious if you remap it’s but it’s always been that way.