I'm very happy to say that we've just made the Xamarin version of the Realm mobile database engine publicly available after a few months in private beta. Read the launch blog post for more details. We have a Xamarin Component in approval and you can just install with NuGet (package named Realm).
I'm very happy to answer any deep technical questions as I've been one of the team on this for about 10 months. Apart from giving Xamarin users access to a great product, we have learned a lot about implementing LINQ, using the Fody weaver to generate code and interfacing to C++.
You can use Realm either from PCL or directly in native code.