Yes, but not for long. I is designed to run off AC power and the battery is for backup when you have power outages. You will have a much better experience if you can keep it plugged in. 

So long as it has a usb port there is no reason you could not. That being said, I have never directly powered any device from mine. I use it to charge my power banks and then use those to power other devices. Loss of a power bank because of spiked or fluctuating power (in and out of shadows, fast moving and intermittent cloud cover) may cause damage to devices that are directly connected. But, a power bank is a heck of a lot cheaper to replace. 

Yes, the height can be adjusted up or down by turning the adjustment knob. 

You don't have to collect the bracket. You can buy them directly. The packaging now contains the clip. If you encounter any problems during use or you are missing any accessories, please contact our after-sales staff. We will reply your problem as soon as possible and solve it. 

It does not come with a stand, just a background cloth and 4 spring clips.