I do not know why you are not responding, but you are not charged per question, per response, nor per answer. So after I give you my answer, you can continue to ask me questions without additional charge until you are satisfied. I apologize if it is a site issue that you posted and the post did not go through.
Unfortunately, the ESTA visa is one of the worst visas to have. You cannot extend your stay and you cannot change status to any other non-immigrant status while in the U.S. (with the possible exception of a U visa as the victim of a serious enough crime or an S informant visa). You MUST leave the U.S. to apply for the proper visa to come back.
As to an immigrant visa, that's a different story. If you are in a relationship with a U.S. Citizen and you marry, then yes, you can stay and "Adjust" status to U.S. Lawful Permanent Resident. Change of status and Adjustment of status are different things under the law.
After you marry, you will need to file an adjustment package. This includes the following forms: I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), I-131 (Application for Advance Parole), G-325a (Biographic data - one for each of you), I-693 (Medical exam that a certified doctor must fill out), and I-864 (Affidavit of support). You will need to file each form with supporting evidence and appropriate filing fees. You can find these forms at www.uscis.gov/forms.
The supporting evidence that you would file would be birth certificates, marriage certificate, divorce certificates if either of you have been married previously, proof of your spouse's U.S. Citizenship, proof of your legal entry into the U.S., and financial documents of your spouse to prove their income over the last year at least.
In about 3 to 5 months after filing, the work permit and Advance Parole (travel permit) should be issued. About 5 to 7 months after filing the interview should be scheduled (though now it is taking longer, so maybe closer to 7 to 9 months). If all goes well, a few weeks later the U.S. Lawful Permanent Residency card (green card) should come in the mail.
Please let me know if you have any additional questions as I will be happy to respond, but because this case is the type of case that I love to handle, I will now send you a low-cost offer so that I can pass on my personal phone number and email. I have multiple services available to you from document review to full representation and all at very reasonable prices though I can only discuss those in private, not an open forum like this. You won't be disappointed as these are my favorite cases to do and have been doing them for many years. If you decline, no problem, you can ask additional questions without any additional charge. But PLEASE remember to leave a positive rating for me. You can do that by clicking on the 3rd, 4th or 5th stars if you see them, or the smiley faces if you see them. Also, a bonus is always appreciated if you feel I earned it. And finally, your question does NOT close just because you leave a positive rating. I can still answer additional questions for you without additional charge. Thank you for your understanding.