Safety of powering 5V circuit of 240V main outlet using adapter
If it's a general purpose USB "charger", then it should be fine.  Since those don't know what device will be hooked up, they have to provide regulated 5 V as USB devices expect.  If it's a charger for a specific device, then it might play some games, but even then likely not.

You can always check this.  Use a voltmeter to read the output power voltage.  That should be close to 5 V.  Then load it with 1/2 amp or so and verify that the voltage doesn't dip much.  A 10 &Omega; resistor accross 5 V will draw 1/2 amp.  Note also that it will dissipate 2.5 W, but you only need to hold it there just long enough to watch what the voltmeter does.  A little 1/4 W or 1/8 W resistor might blow up quickly, but a 2 W resistor will be fine for a few seconds.

The current rating only tells you how much the charger can deliver.  It is up to the device what it actually takes.  A 2 A charger is therefore a superset of a 1 A charger.  If your device only needs 1 A, then both will be fine.  Note that real USB only guarantees 500 mA, and that is after some negotation.