US Immigration from Malaysia

We just got married so I'm (american citizen) am wanting a healthcare plan to cover my wife and her child. I'm going through the healthcare marketplace to do it. I submitted the application and it said we are eligible but her child isn't? But "May be eligible for Medicaid based on this month's household income".

Kinda confused by what this means. So if I enroll in a plan, our daughter won't be able to use our plan for free check-ups and such? Is medicaid/chip even available to her as a non-citizen or green card holder? Do I just need to call the marketplace, or is there something else to it? The "next steps" section for her says "Wait for more information from your state agency about Medicaid coverage. You may need to provide more information to the state.". So maybe I just wait?

I googled this for 30 min and couldn't find answers. I read before its easier to change name during marriage as opposed to any other time, but I can't find information on how thats done. We live in Alabama.

Also, is it ok to do this before she gets her SSN? We applied for it 10 weeks ago but still haven't received it.

My petition isn't approved as of right now, but I am asking in advance. Since the new I-485 for AOS cases has integrated I-864W into I-485, that leaves the consular cases out. Will I-864W still work on the consular side for those outside the US, or do I have to do I-864? (Filing for children only)

I thought it only takes 2 to 4 weeks, but its been almost 6 weeks now and still no SSN. We applied in person on Jan 6th. We called back last week and they said they are still processing it. Is this normal?

I accidentally got some blue ink onto my I797 extension letter:

Am I blowing this out of proportion or might this give me issues when attempting to board or re-enter the US?