What happens if a resistor is removed from the circuit (Picture Attached)?

Do you mean remove or do you mean short out?

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When you "remove" a part, it means the part is not in the circuit anymore. I suggest you look up the definition of "remove". You have gotten three correct answers.

I suggest you reword your question. "Examine the changing current" is pretty meaningless.

All of the components in the circuit are functionally necessary. There are no aesthetically pleasing parts.

If any part is removed it does not function.

remove either resistor and the LED will never be lit.

150 opens the collector circuit, which the LED is in

500 opens the base circuit, transistor can never turn on.

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"Max current supplied is 500 mA ... Will the LED or transistor be damaged?" max current is limited by the 150 Ω resistor to about 20 MA.  Where did you get the 500 mA number?

"'remove' does not mean make an open circuit."  YES, it does. remove a resistor always results in an open circuit. You need to learn some basic circuit principles.

"the question is to examine the changing current." don't know what you mean by this. Do you mean varying the resistors? over what range.?

150 Ω determines the LED current. lower values could damage the LED, depends on the LED specification.

500 Ω determines the base current. What happens when you modify it? depends on the circuit in the IC that drives that output. If it is a 0 to +5 volt signal, that resistor could be a lot larger. 2N2222 has a high beta, so to drive 20 mA in the collector, 0.1 ma in the base is more than enough. If the drive is +5v, that resistor could be as high as 5v/0.1ma = 50kΩ, lower if the drive is lower voltage.