A:AnswerYes it includes the holder for your cell phone. This piece clips onto the controller and has a lot room for the larger screens (using a Samsung Galaxy S20+). The clip is also designed with openings to allow either the USB or the Micro USB to be plugged in (which comes with both as well).
A:AnswerIf using the wired connection for control, you can't use the controller and charge the phone simultaneously. The controller function and recharge function use two different ports on the Moga itself.
If using the controller in Bluetooth mode, then yes, you can be using Bluetooth and have the recharge USB connected.
A:AnswerI've had this controller for about a month now, and the battery stays up around 100% for a long time. I play Minecraft PE on my android tablet, I connect the controller through bluetooth and I play for about 4-5 hours each day. Battery lasts long, how long? I'm not sure haha, but I don't think you need to worry about it in particular because it lasts for a while on a single charge.
