Many of us would have gone through similar issues, but even after going through following most relevant links reference link1 and reference link2 , I am not able to resolve.
As far as typings is concerned, it is no longer used. All or most typescript declarations are moved to npm itself and you install them as npm install @types/package_name
.
https://www.npmjs.com/~types
https://github.com/DefinitelyTyped/DefinitelyTyped/blob/master/README.md
If you need typings folder you could try
npm install typings
you can also referance type declararions through
//
in typescript