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?
Yes, you can use SQLite on the iPhone. Since the database is just a file, you can add the 50 MB file to your application, and that's it. SQLite's performance on the iPhone is good, in my experience, although YMMV depending on your exact table layout and indexes.
In my opinion, it's definitely worth checking out the FMDB wrapper suggested by Galwegian; it makes the programming quite a bit easier than directly using SQLite library itself.
Although 50 MB is way below the limit, be aware that a 50 MB application will take some time to download for people, and people cannot install it from the AppStore without either a WiFi connection or iTunes.