Is there any way I can for example say:
Alamofire.Manager.cancelAllRequests() or Alamofire.Manager.sharedInstance.cancelAllRequests()?
You should use the NSURLSession methods directly to accomplish this.
Alamofire.SessionManager.default.session.invalidateAndCancel()
This will call all your completion handlers with cancellation errors. If you need to be able to resume downloads, then you'll need to grab the resumeData from the request if it is available. Then use the resume data to resume the request in place when you're ready.