Firstly your heading should be differences; different is an adjective.
Have I forgotten? Correct; note the spelling and question mark.
Do I forget? OK, but more natural would be 'am I forgetful?'
Did I forgoten. Incorrect. Did I forget or have I forgotten?
Had I forgotten? Correct.
Example: Had I forgotten to write this then you could ask me if I do forget frequently, but then I already know that I did forget and that I have forgotten many times in the past.
See if you can work out why I have written that sentence.
Interested in Language