Are typescript type definitions required?
It appears that the definition files are required, is this always the case?
No. If the module does it properly using the typings property it would just work. More: https://basarat.gitbooks.io/typescript/content/docs/quick/nodejs.html
The rx npm package includes the definition files. Can typescript automatically search the node modules folder to find them without me having to explicitly reference them?
Only if they have typings setup properly ... which they don't.