Can I use and external power supply and USB at the same time on my Arduino?
Yes, you can simultaneously connect external power supply and USB. As explained in one of the answers, that you linked, the Arduino chooses it's power input through the supplied voltage on Vin/barrel jack. Vin has no direct connection to the VUSB, so the USB port will not get any voltage from the external supply, thus it does not get damaged.
BUT: Your thinking is wrong. Clearly your LEDs need more than 500mA. This current should never flow through the Arduino. You can easily fry the protection diode or the voltage regulator (which is an inefficient linear regulator), if you connect all the LEDs to the 5V pin. One GPIO pin can only provide about 20mA (40mA at absolute max, you should stay below 20mA) and only 100mA through all GPIOs together. They are not made to provide power, but for switching.
Instead you should connect the LEDs outside of the Arduino to the power supply. If you want to use the specified 9V power supply, you need to buy a buck switching voltage regulator, which gets the voltage down to 5V for you. Make sure, that this regulator is rated for a current significantly higher, than what you need.
How to control the LED then? That depends on your LEDs. If you just have some bare LEDs, you could use a transistor to switch the higher voltage from the Arduino. If you have a plain LED strip you can also use a transistor. Best use a MOSFET for this. If you have an addressable LED strip, just connect the power lines to the 5V output of your new switching regulator and the data line to the Arduino.