No Title
Yes, you can enter.
No, you do not need to put anything in "THE APPLICANT’S NATIVE COUNTRY IF DIFFERENT FROM COUNTRY OF BIRTH". If you were born in an eligible country (which you said you are) that will entitle you to enter the Diversity Lottery.
You only need to fill "THE APPLICANT’S NATIVE COUNTRY IF DIFFERENT FROM COUNTRY OF BIRTH" if you were born in an ineligible country and would like to enter under another option (ie. parents place of birth).
I\'m no expert in the immigration field, however, I just won the right for a GC in the recent DV-2001. I filled in the forms myself and as long as you follow the strict instructions you\'ll have as good a chance as anybody in winning a GC. Also, hiring a lawyer will not make any difference whatsoever, they will only ensure that you fill the forms correctly (any intelligent person can do this themself).
A