A:AnswerNo, it does not have a headphone jack. It has a mic input. It does have USB-C, however if you'd like to charge via that port you need a special charger.
A:AnswerDepends on your usage. I'm not a hardcore user so for me it lasted all day and still had battery remaining. And by all day I mean Christmas where we had a family Christmas in the morning where I did a few videos and several pictures, then took a several hour break before getting it out to take random pictures at the in-laws and then video again of Christmas presents with the whole family. For straight video recording i'd guess several hours but a giant benefit is it charges off of usb C which means my phone charger will charge it and my battery pack will keep it alive too.
A:AnswerYou have a few options. You can get a double bracket that you can mount the camera and mic and attach it to a manfrotto pixie or you can get the rode wireless go and Clip it to the bracket on the back of the screen when flipped up.