To register (register), you can create a method in a user controller that does just that. Or you can customize the Devise sign_up page to look better in mobile mode and do web-view registration in the app.
As for Doorkeeper, either follow the normal thread you linked to, or simplify it. What I did was
activate the update token - this will allow the user to get their access token and update token, the token used to regenerate the access token after its expiration. Thus, you do not save the user login registration in your application, but only tokens.
white label config/initializers/doorkeeper.rb, skip_authorization, . , :
skip_authorization do |client|
whitelisted_apps = ['app1_id', 'app2_id']
whitelisted_apps.include? client.application.uid
end
, .