The simple answer to you question is yes you can do those things but no you cannot do them in the way you want. You would not be able to launch to the app store and then once the app is downloaded launch into a specific place in the app. This is mostly due to security.
So let me explain, there is a method that you can call UIApplication.sharedApplication()canOpenURL(url)
which will return a Bool
on wither or not you app can open a url. If it comes back as false then you can assume the app does not exist on the device and you can call UIApplication.sharedApplication().openURL(url)
where your url = NSURL( https://appsto./Path/to/your/app) then "The User" will have to click the download button.
Then if they try the action again you can call
UIApplication.sharedApplication().openURL(url)with
url = (yourapp://).This will launch your application.
Now for launching to a specific place in you app you will need to setup schemes for your app. There is a decent tutorial on doing that here http://www.brianjcoleman.com/tutorial-deep-linking-in-swift/ and also a short synopsis of what you can do found in another answer to deep linking here Confused with IOS Deep linking
So you can get most of the way there but with Sandboxing
you will not be able to launch the store, download the app and launch the app all in one move.
Hope this helps, cheers.