I bought the B330. As I understand it, it's the same mouse in a very slightly different design. Logitech lists the M330 under mice "for me" and the B330 under "business".

USB 3 connections can interfere with Unifying plugs. Solution: Insert the Unifying plug in the USB 2.0 port if available, or distance the plug with a USB 2.0 extension cable. Another possibility is to insert a USB 2.0 memory stick in the adjacent USB port.

It worked for me right away, yes.

If you are sure that the wireless connection is stable, I would make a warranty claim (you have 24 months warranty). Logitech products are often very durable and a warranty claim should not be a problem. I'm not sure, but I can imagine that you will lose the warranty when you open it. https://www.digitec.ch/de/ReturnsAndWarranty