Can my eyesight gradually change so that I no longer will need my glasses?

Eyes. Yes. In some people, the prescription gets better with time. This is not common, but it may happen.
Yes. You are correct. The anatomy of the changes over time. For example, the direction of astigmatism changes over time to become horizontal in many cases. As the lens inside the eye changes slowly over time, it may change to either improve near or distance vision. When cataract formation leads to improvement refractive error (not vision), it is called "second sight".