To clarify:
1- Yes, you should have written "none" as that is preferred to keeping it blank, but they won't reject your application because of it. It's just good practice and "none" is much preferred by USCIS because they don't want to guess why you didn't put a number there (are you trying to hide a previously rejected I-140, etc etc).
2- A numbers: Yes there are 2 types of A numbers, as you all found out. If you apply for an EAD under a non-immigrant visa status (J-2, OPT, etc), you will receive a nine-digit A# that usually begins with a "1". When you file for immigrant benefits (I-140, I-485, EAD based on I-145, etc), you will receive a different 8-digit A# (it's sometimes 9-digit but the first number is "0"). So basically, if you are ever applying for an immigrant petition or benefit, as opposed to a non-immigrant based benefit, and you have an A number based on the non-immigrant benefit (9 digit number that does NOT start with a "0"), then you can write "None" in the field requesting the A number because you will be assigned a new 8-digit (or nine-digit with the first being "0") A number which will, as mentioned above, stay with you for life.