We were CHALLENGED on that issue by USCIS. He ultimately decided to return to China rather than face the court proceedings.
No the green card is NOT automatic with a K2. The application MUST be filed separately as I have stated.
The poster here will need to do the same regardless of whether K1, K2, or F1.
The APPLICANT pays for the original I-130 or "fiance" applications. The beneficiaries do not.
The poster here is a BENEFICIARY, not an applicant. I believe her misplaced concern is with the COST of the green card. That COST is borne by the American applicant.