Is it possible to get the images from the Android Gallery via realm.io, or can I only access my own models I stored into the realm database?
You can only access data you stored in Realm yourself. So while you could store gallery images in Realm if you wanted, it is probably a bad fit as images are usually best stored in the filesystem (this is true for SQLite as well).
Normally what you can do is to store the path in Realm and the image itself in the filesystem.