Handling editor sent me a review invitation From your experience, is it some kind of sign when handling editor of your manuscript (which is under review) sends you a review invitation for other manuscript?
Yes, it's a sign that they don't think you're a complete crank. That may not sound like progress, but it is a good thing nevertheless. It doesn't mean anything else about the handling of your own paper.

And remember, part of the art of getting published is keeping on the good side of editors.