To my experience, you can find these astral cords attaching us to anything that we are emotionally attached to. If you look hard enough, you can find one for every friendship, acquaintance, loved one, relationship, etc. As we spend our lives attached to our bodies, there is quite a bit of emotional baggage creating the "silver cord" that links our body to our spirit. The less attachments in this life, the less hold these cords have on us, and the more freely we can roam spiritually. Somewhat akin to Buddhist concepts.
As for changing form astrally, this is all a matter of visualization. While the astral self and other spirits lack any true form, not being a substance of matter, the mind frequently processes the perception of one's own spirit, or any other spirit, visually to help us understand what we encounter. As such, the perception usually dictates how we visualize ourselves or anything else. Thus the basis for some concepts such as otherkin, where the individual truly believes that their spirit is associated with various creatures of mythology - fairies, angels, etc. Similarly, if you are able to control your perception, you can alter the visual image you have of yourself and project this outward - what we perceive of ourselves is often influential in how others perceive us, much as in the physical world our style of dress and such is born of our self-perception and therefore influences how others perceive us at a glance.
This will to emotionally and willfully influence perception of the self and others is at the heart of magic - not only astral projection.