Is it normal/recommended to have more
  than one activity in Android app?
Normal? Yes. Recommended? That depends on the app.
in my opinion, it's somehow strange to
  have this model of data exchange
  inside application
What do you do with Web apps? Well, you keep your model in a central spot (server) and you pass small bits of context data (URL parameters) in links between major units of UI (pages).
What do you do with desktop apps? Well, you keep your model in a central spot (database) and you pass small bits of context data (e.g., constructor parameters) in links between major units of UI (windows).
What do you do with Android apps? Well, you keep your model in a central spot (database, ContentProvider, etc.) and you pass small bits of context data (Intent extras) in links between major units of UI (activities).