A:AnswerYes, but if you have multiple devices paired to them, you have to manually connect them in PS4 settings. I haven't found a way to have them switch automatically from my phone to the PS4.
A:AnswerYeah that's a pretty big design flaw. I left to go for a run so I didn't bring my case and this flaw combined with the "feature" that they automatically disconnect and power off after a couple minutes if you don't start playing audio right away meant my only option would have been to go back home for the case.