Does Swift compile to native code?
Swift not only compiles to native machine code but it has also been designed specifically for it. Unlike e.g. Java which has been designed specifically as a JITed language. By that I mean Swift achieves best performance with ahead of time compilation while Java benefits most from JITing.
There are many reasons for these design choices but among them is that Swift has a much bigger scope than managed languages like Java. It is supposed to work on both desktop computers and phones with more restricted hardware. You can use Swift as a systems programming language unlike say C#, Java or Python because it has little runtime requirements and allow fairly detailed control of memory. So in theory one should be able to build an OS kernel with Swift which would be difficult with say Java.
Yes, it compiles to machine language by way of LLVM Bitcode and, as @connor said, runs on top of the Objective-C runtime.