What is the range of bluetooth transmission?

The max is about 10 meters (about 30 feet).

thank you.

and, but if there is a wall between ? then..?

In your case I would say about 12 feet because that wall, yeah that one. The one to your right, is pretty thick. I think that paint on there, I think I see some yellow which generally means lead. lead absorbs bluetooth singal like a sponge.

Scrape that paint and perhaps consider making a window there.