Android Architecture Questions

I've been reading about architecture to android projects. And I found some stuff, but I guess I misunderstood some concepts or not even understood at all.

One of my questions is about handling api objects, if I have a local database, Should I use the same object from api to store in local database?

I'm also looking for explanation about why use MVVM or MVP, actually they looks like different stuff, I have figured out that MVP is a pattern more concerned about handling UI responsibilities, MVVM I think is oriented to handle communication between UI and database. So I misunderstood the concepts or it make sense?

The last but not least important topic is about dependency injection, I have read about the concept and this question came to my mind, why should I use any framework as dagger to handle this, if I can handle this pattern by myself, once it's not thaaat complicated?