It's because of the circuit used inside of the multimeter to create a virtual ground at approximately Vbat - 6.2V, or about 2.8V for a 9V battery; this basically means the COM terminal on the meter is at 2.8V relative to battery ground and readings will be offset by this.
I tried with another meter to measure its 9V battery - it read 6.08V, which is very close to the predicted 2.8V drop.
The USB wall charger is capable of providing up to 1.3A. Current draw is based on load, not on upon what the supply can provide. Obviously if a load requires more than a supply can provide, the load may not work correctly, or the power supply may fail (and cause damage if not protected).
A voltage meter places a high resistance across the test leads so that you can get an accurate voltage reading without drawing much current.
A current meter places a low resistance in series with the device under test so that you can get an accurate current measurement without adding a significant resistance. Your meter should have fuses for various current measurement ranges so that you don't damage the meter.
When you measure current provided by the wall charger, you should do so with something being charged. If you're just measuring current with your meter as the only connected item, you're effectively placing a short across the charger's terminals and it will therefore be unable to supply sufficient current.
When you connect your meter to the supply with any range that's under the 1.3A supply capability, you should theoretically blow the fuse in your meter for that range. I can't speak as to why the meter is showing unusual numbers for each range.
Connect a load to the charger, then insert the meter between the load and the charger to get a current measurement. Always start with the highest range and progress to lower ranges as applicable. Your meter measures 10A max in the 10 range, and the next lower range has a max of 200mA. Therefore, I would not measure current from your wall charger on any range other than 10 until you know for certain that the load is drawing less than 200mA - at which point you can safely switch to the 200mA range.
Note also that your meter indicates that the current measurement port is unfused and that it will tolerate a maximum value for only 10 seconds. Therefore, you might be getting unusual readings because the current measurement circuitry has been damaged. If you have only been very briefly measuring current with it, it might still be functional.
Best Answer
General rule for measuring currents with multimeters:
Here's a very good article by Analog Devices' applications engineer James M. Bryant about using standard multimeters written for beginners with much attention to details.