Yes, you can scroll to Add New City, and then search Google for the longitude and latitude of your location and add it, you can click up and down to get the exact numbers.

Yes, the default shows Gregorian, and when you need to check the Hijri you click the "up" button once and the Calendar will change to Hijri and after a few seconds return back to Gregorian. You can change the setting to show Hijri as default from the Calendar settings

Yes, you just need to choose your location and set the correct time and date and the rest the clock takes care of

Yes, you only need to change the DST to ON or OFF and the times will be displayed correctly automatically, an advise to compare prayer timings to your local Masjed timing, and if there are a few minutes difference you can adjust that using the Azan safety time setting in the clock