It depends on how you feel about it and what you want to do with it. Cable connection gives better quality, but you have to be completely dedicated to the music to notice the difference. For example, if you want to listen to music while working, it's absolutely no problem. If you go into music processing, you'd better use a cable version.
I recently bought the adapter. I can't answer whether it is compatible with the Logitech M705 mouse, but I think it should work under Windows. What I have found is that it is not compatible with MAC/Appel, no drivers can be installed. See also questions about Speedlink USB Bluetooth 4.0 Adapter at Digitec.
No, this Bluetooth adapter is only for keyboard and mouse with Bluetooth 4.0.
For your concerns, you need to buy an adapter from Plantrononics.
Greetings
For me, the question would rather be to what extent this is relevant...... USB 2 already has a much higher transmission speed than Bluetooth 4.0. Therefore, from my point of view, not relevant.