If I put an inline function in a .h file, then include that in the bridging header, can I invoke it in Swift? (Answer: Yes) But will it still be inline when invoked in Swift?
The compiler will do what it wants but generally the answer is yes. This is part of why the atomics libraries and math shims that go down to C use header only inlined modules. So at least in release builds it can be fully optimized.
See this for example.