Is it possible to make a big 50MB database native on the iPhone? So that it can be searched very quickly in a smart way? With SQlite?
By all means use SQLite. I find it very easy to use. If you need some sample code check out http://tetontech.wordpress.com/2008/06/28/iphone-objective-c-sqlite-development/
If you would like an easy to use wrapper check out QuickConnectiPhone. This framework has a wrapper that you could pull out and use.
https://sourceforge.net/projects/quickconnect/