The Shadowrun Astral plane is totally unlike DnD Astral (at least Planescape Astral). Think spirit world: everything living gives off an aura, while "dead" things appear shadowy and insubstantial. Dual-natured creatures, such as spirits, appear with extraordinary clarity. For the most part, however, the Astral plane is a spiritual copy of the real world; think DnD Ethereal/Shadow planes.
Metaplanes are more like DnD inner/outer planes; each has it's own appearance, logic, and rules.
Complex Forms and Programs behave more-or-less identically.
A tip from my standpoint, have a general idea of how the rules for any given thing work, but have your players learn the specifics as they apply to their characters, and inform you as needed. If you feel that you can trust your players (and if you can't, why play with them?) this system tends to work wonders for taking work load off of you.