Cognito external provider with events

I am trying to integrate Cognito as my auth service.
i would like to have

  1. No password with phone number SMS authentication
  2. facebook sign in
  3. google sign in.

for 1 i made a custom flow with triggers. in the triggers i create the challenge and challenge verification as well as creating a user entry in the dynamoDB for more user data

the issue starts with the external providers…
ill start with saying that the whole identity pool and user pool separation and what is each responsibilities and capabilities are probably the most un clear of all AWS services.

i dont know how to make a trigger for sinin through google external provider in the user pool

i noticed i could define external provider both in the identity pool and in the user pool.
also in the identity pool i could use “sync triggers” but not sure when is it running and tried to trigger it when signed in with google but nothing happend.

how do i connect the provider defined in the user pool with the identity pool?

is there anywhere a good course or documentation about this service?

is there a way to invoke a lambda for every user created in the user pool?

because it is very confusing!!