Is it possible to get information, such as the block attributes, from other blocks from within a registerBlockType call?
E.g. if I have a block with InnerBlocks as the content, is it possible to get attributes from the blocks inside that InnerBlocks, or vice versa?
Yes it is possible if you manages your own store inside Gutenberg which is actually a Redux store. @wordpress/data
It is recommended to keep logic of your multiple blocks separately in their own attributes (that's why they are blocks). For re-usability purpose you can make React components which can be used inside different blocks, in this way attributes of your block can be passed to the props of React Component.