What is the min iOS which works well with Swift 5.1 or incoming Swift 5.2?
Are there any references to check this?
A similar question has been asked before, when Swift 4 came out. You can find the question and answer here.
Having that said, the swift.org site and the release notes only specify the compatibility with previous Swift versions, the operating systems and the toolchain (Xcode). So, a straight forward answer can't be given to this question.
Since Swift 5.1 is compatible with Swift 4, you can safely assume the code will run iOS 11 and probably iOS 10 as well. There are, however, some incompatibilities between Swift 5.1 and Swift 4, see for the details this link. I think you should also be aware of the fact that as of iOS 11 32 bit is not being supported anymore.
The next issue you will definitely run into are the deprecated functions in iOS. You have to build your code in the productive version of Xcode and that tool will throw errors and warnings for deprecated functions or variables being changed. For instance, the key "[UIImagePickerControllerOriginalImage" has been changed to "UIImagePickerController.InfoKey.originalImage". at the moment Xcode 11.3 doesn't let you specify below 12.1, so you will run into these problems when updating source code written in an older version.