Yggdrasil
Form. There are loads of conceptual maps and illustrations of the Worldtree that you could take inspiration from! By definition, a worldtree is big enough to serve as the rotational pole of the world, be it spherical, flat, or any other shape you have in mind. Limbs can indeed serve to host multiple worlds on their branches and leaves. The tree itself can be straight, which might be suggestive of highly stratified ecologies, or perhaps twisted & curvy which might be suggestive of multiple ecologies within a variety of zones. Multiple trunks could suggest a branching system of twin or mirror ecologies.
Magic. You don't need to invoke magic, if you don't want to. The world is what it is. If magic isn't part of it, then you leave it out. This is one of the keys to understanding the art of the geopoet, the worldbuilder: you don't need to make a world that could be real in order to make a world that is realistic.
Science. The science will follow the reality you have established. Even in the real world, science can do no more. For example, you mentioned a sun orbiting the worldtree. This suggests that there are daily cycles of light and dark. You could also define other motions that would create one or more systems of seasons & ages. You might also broaden the scope and see if this worldtree system is a part of a larger worldforest of interconnected worldtree systems.
Particulars. The scope of this world is entirely up to you. The worldtree could be, according to our perception, very tiny or it could span light years. Worlds can be connected in a variety of ways, or be separated as determined by the design or some event that unfolds. The tree itself could be static or mobile, passive as a mere infrastructure or active as an integrated part of the whole oecumene. There are no limits here.
