The 500 mA rating would be worse case. There's no reason for the manufacturer not to put a generous number. It's not as though the power supply or wire would be any smaller or cheaper for 300 mA than 500 mA. If you make wire that will only take 300 mA, it will fall apart when you look at it. It would be a different story for bigger ratings where they would be more accurately calculated.
You are confusing the voltages. You have the power supply voltage, the battery voltage and the resistor voltage. In a simple circuit like that, power supply voltage = battery voltage + resistor voltage
With a 6.5 V supply, and 3 V of battery, there is 3.5 V across the resistor. A 12 Ohm resistor means that 3.5/12 = 292 mA charges the battery.
If you supply it with 5 V, still with a 3 V battery, that leaves 2 V across the resistor, and the charging current is 167 mA, so slower charging but still almost certain fast enough for most uses.
The surface mount resistor does connect. The light green tracks aren't visible under the white silk screen printing, but they are still there. I guess that the resistor is so that the handset can detect the charging base even if it's not plugged in, so that it will still answer a call when picked lifted off the base or hang up when replaced.