Yeah it's been around for a long time - although many of the earlier version were rather awful. There's different methods, and not all of them use neural networks.

But there's software to do it with a decent camera that works okay, you'd be better off with a green screen though in most any situation.

In MS Teams you can blur the background while video chatting. So I'd say yes, it exists.

Depends on the background by method. At thr very least chroma key and edge detection qualify - define a target and take them to their edges - just with signal processing and no learning.