Are all molecular structures symmetric? Are all molecular structure symmetric either in relation to a plane within itself or in relation to other molecules? Are there any completely asymmetrical structures when looking at molecular geometry? Are there any studies into the reason for symmetry?
It is not quite clear what do you mean by "in relation to a plane within itself or in relation to other molecules", but I think the answer is no, not all molecules are symmetric. Many of them belong to what is known as $\mathrm{C}_1$ point group, or, in other words they are are totally asymmetric. For more information on molecular symmetry and point groups read this Wiki article.