Yes, in the sense that the results are doubly compressed.

No, in any meaningful sense that I would have an issue with. The headphones have the appropriate BT codecs for high definition audio (the 3 even more so, aptX et al), and the end results have been on par with my wired AT-50x.

You can try double and triple compressing a 320mbps mp3 file and you'd hardly notice any change. Of course such compression algorithms are not omni-potent, but it's close enough.

At a good enough bit rate (256 and especially 320), mp3s are indistinguishable from "CD quality" (which also throws away data in the sense that it quantizes the analog signal, but it doesn't matter there either), and all blind A/B/A tests have shown that.

In headphones that cost less than $1000, and for everyone over 40 that's even more so.

Audiophiles excepted of course, because they have magical unicorn audio senses -- even when they can't use them on a blind test.