About the same amount of time as the 5W wall charger that comes with iPhones.
4000 mAh is just larger than a typical mobile phone battery. It takes about 3 hours to fully charge.
Yes, the powerbank supports charging while it is plugged in and being charged itself.
According to the TSA you can up to two spare batteries per customer in carry-on luggage. These powerbanks are rated < 100 watt hours which means they can be packed in checked luggage as well.
Not really “extra” but the powerbank comes with two built in cables – one lightning for your iPhones and the other micro-USB for most android devices. And you can always buy a nice three pack of high-quality Paracord Lightning Cables here.
Yes, the powerbank is designed to be charged via USB with any standard micro-USB cable (included) and USB wall adapter (not included).