how to open another instance of the Vue, while an image is being rendering?

You can't open multiple instances. What you can do, though, is use the external renderer to render your scene, it will render to disk in the background, and go on working inside Vue.

I open Pro Studio and work with it all the time while Infinite is rendering.

But remember, the external render will stop rendering the more you use the processor.  It's better to leave it alone and wait for the render to be done before starting a new project...

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Infinite and Pro Studio are 2 different apps, not 2 instances of the same app.