purescript-refract VS purescript-concur-core

I've worked on something similar for Purescript (https://github.com/pkamenarsky/purescript-refract) and recently also Haskell (https://github.com/pkamenarsky/refract-replica, no docs yet but the API comes very close to the Purescript version).

1. Application wide state is easy since you can always access state from parent components in child components. The problem occurs when you want to update parent state from child components.

Fortunately, you can make your own abstractions in Concur. For example, you can use a "Wire" - which lets multiple child components share and update parts of the parent's state (https://github.com/purescript-concur/purescript-concur-core/...). Note how this abstraction just uses the high level Concur API, and doesn't depend on the UI backend. With a wire the code might look something like this -

  -- A wire into parent's state, accessible using `with`, and updateable using `wire.send`

Have you looked at signals? AFAICT they are exactly what you are looking for. A signal is just Cofree widget (https://github.com/purescript-concur/purescript-concur-core/blob/master/src/Concur/Core/FRP.purs#L26).