Hi Prasta,
Yes, there is a reason, or several reasons in fact, why we go up the spine during inhalation, and down during exhalation. They are covered in this lesson:
Which way is up? You could force kundalini more quickly by using other methods, or differnt breathing techniques, but the art of awakening kundalini is not about forcing it to awaken as quickly as possible. Kundalini is a powerful force and if it is not awakened carefully and in a safe manner, then effects can be painful. So the art of awakening kundalini is really about preparing (purifying) the body to be ready to be able to handle the increased flow of prana through it. When the body is purified sufficiently using effective spiritual practices, kundalini awakens automatically and the process of spiritual transformation is fast and pain free. That's what the AYP techniques are designed to do.
As far as Puraka, Rechaka, Kumbhaka pranayama with a 1:4:2 ratio goes it is a form of pranayama designed specifically to awaken kundalini. It does this by using breath retention (kumbhaka) after exhalation when prana is being held momentarily at the root chakra. Baahya kumbhaka, or breath retention with the breath held out of the body is a practice that Yogani specifically advises against. This inhale/ exhale/ hold 1:4:2 practice does not do much in terms of preparing the body to be ready for awakening, and concentrates instead on causing the awakening to happen. In other words, it isn't especially safe.
In AYP there are two forms of breath retention (kumbhaka) used, but they come in much later on after the groundwork has been laid by other practices. Kumbhaka is a very powerful form of pranayama and needs to be used wisely in order to be effective and safe. In AYP, kumbhaka is always combined with Spinal Breathing Pranayama and only used after inhalation (antar kumbhaka). There are two specific techniques used, Yoni Mudra Kumbhaka and Dynamic Jalandara. By combining breath retention with Spinal Breathing and using it only after inhalation, prana is drawn to the ajna chakra during kumbhaka. This is a much safer way of purifying the body and awakening kundalini than attempting to activate the root with kumbhaka. In AYP the root chakra is activated in other ways which are much more gentle such as siddhasana, mulabandha and Spinal Breathing Pranayama.
So with your last question, don't attempt to push prana through the shushumna (central channel). Simply trace the nadi with your attention, that is enough. Again, it is about purification rather than attempting to force anything. It is about getting the horse in front of the cart. The horse, in this case being the gentle process of spiritual purification and the cart being the more dynamic energy of spiritual transformation (kundalini).
Christi