Please, let me interfere into this thread as my colleague is out of the office.
I've reviewed the entire communication since the beginning of the thread, and to me It is not clear what kind of mobile applications you are going to test. Can you confirm on this, because with Test Studio for Mobile you can test mobile native, hybrid or web applications on iOS or Android devices. For each of those, there are some specific steps you need to follow and execute in order to build a correct testing environment - for more information check out our Getting started article
With the above said, I see that Elena gave you information how to test mobile web applications.
I would guess that this is not your case and you want to test a native or hybrid applications already installed on iOS device. As I understand, you have installed the required Mobile agent app to your iOS device and you can connect the agent app with Mobile testing studio using the USB connected device as it is described here
However, when you start to record a test and specify the application the connection between iOS device and the Mobile testing studio breaks. Please, let me know if my assumption is incorrect or you're doing something different?
To address this and answer your last question, yes, you can test iPhone applications with Windows desktop but you need to ensure a couple of prerequisites which are described in the already mentioned getting started article.The only thing that you cannot do with Windows desktop and requires the use of Xcode on MacOS is the instrumentation of iOS application
However, if the iOS developers in your team has already installed on your iOS device an instrumented version of iOS application, you will be able to record your tests agains this application on Windows desktop utilising an USB connected device.
I hope this helps. Please, let me know if you will require further assistance.