I very rarely use Windows, but on Linux my headphones use either LDAC (Sony) or aptX HD (or something like that) for the Shure. On my mac and iPhone they use AAC. Never had any issue with any combination.

Regarding the keyboard, I do feel a slight lag compared to wired, but not enough to bother me. The mouse also seems to have a tiny bit more lag compared to its own dongle; however sometimes it seems very laggy for a moment. This never happens with the dongle. I mostly use these in the countryside, in a detached house with not many wireless or microwave devices around, so I don't think it's interference related. The headphones don't skip a beat, either in the same environment or in my apartment building or office in the city, with plenty of wifis, microwaves, wireless mice, phones, etc around.