Xcode 9 not finding React Native 0.56 or 0.57 - ios

Question

I was working on my first React Native NativeModule. A simple 'Hello, World!' Objective-C function just to get an idea of how it worked. Things were going relatively smoothly, however, it seems xcode lost reference to all React Native files. I thought this problem was probably project specific, so I started a new TestApp using react-native init TestApp, but when I open that .xcodeproj file I have the same issue.
The first error in this new TestApp is in the AppDelegate.m file: 'React/RCTBundleURLProvider.h' file not found but as you might expect it avalanches from there.
I spent the most of yesterday trying out all sorts of potential solutions to no avail.
This might be a false lead, but maybe not, however I noticed Header Search Paths is empty whenever I first open .xcodeproj on a newly initialized project. That being said, I have tried numerous search paths based on answers I have found here on StackOverflow, GitHub, etc, the latest being $(SRCROOT)/../node_modules/react-native/React
I know this problem might be a little vague, but any help would be greatly appreciated. As an iOS developer, I am trying my best to be open to React Native, but continually running into issues such as this is really putting a damper on that.
Thanks!
ps. At this point I wonder if reinstalling xcode, node, npm, and react native altogether would be the surest solution.
Edits for clarity
First I run react-native init TestApp and cd TestApp followed by npm install. I've tried running react-native link at this point as well.
I then open ios/TestApp.xcodeproj. After xcode does its usual indexing I will inevitably be greeted by a red 'React/RCTBundleURLProvider.h' file not found in AppDelegate. Sometimes 'React/RCTRootView.' file not found' happens too. Most of the time, even if this second warning doesn't happen, The RCTRootView * in didFinishLaunchingWithOptions is not colored.
If I try to create a native module like so:
#import <Foundation/Foundation.h>
#import "RCTBridgeModule.h"
#interface Test : NSObject <RCTBridgeModule>
#end
I get an immediate 'RCTBridgeModule.h' file not found.
In other words, Xcode is not finding anything RCT. Autocomplete doesn't suggest anything RCT.
Even with these warnings, I can run the app from Xcode or by running react-native run-ios.
This extra bit, may or may not be relevant:
If I have import { NativeModules } from 'react-native' in my App.js, NativeModules turns out to be undefined.
My current feeling is that there is a crucial step in set up that is not listed in the RN Docs, and for some reason other tutorials aren't touching either. I tried on another computer to the same result.

Answer 1

"Header search paths" being empty is perfectly normal. RN is exposing its headers from the React project. If you go to React.xcodeproj (under Libraries) you can see that the React target has a "Copy Headers" Build Phase, and these headers are being exposed when packaging the library as public headers.
To make sure that your app can use the headers, go to your app's scheme and into the Build section - the React target should be in the list and before your app's target. Also, the Parallelize Build checkbox needs to be OFF. It should be set-up like this out of the box in new RN projects, but maybe something was changed in your project so it's worth checking.
When the build is just starting, and especially on a freshly initialized project, you can expect to see some errors in the IDE during the build regarding public React headers, but they should be gone and resolved once all React third-party libraries finish building and React itself is packaged.
If everything is set-up correctly and it's still not working, delete the DerivedData folder and build again.

Answer 2

Finally linking native code with react-native!
So, I haven't really solved the precise issue, but I managed a workaround.
Previously I was trying to initialize a react-native project and then modifying the Xcode project that was built in the initialization.
I decided instead to approach the problem from the opposite angle of linking react-native to an existing xcode project by following this documentation: https://facebook.github.io/react-native/docs/integration-with-existing-apps.html
I've been able to repeatedly link native code (both swift and objc) to react-native after react-native init TestApp by erasing the contents of TestApp/ios and following the process in the link above.
Thanks #Artal for providing some valuable info on the way it is supposed to work.