Well, today I tried to get some advises, first by phone, no success. Then my daughter and I went to three addresses from healthcare.gov. All three don't exist and nobody heard about them.
I have tried to download my passport page with immigrant visa. No success. Tomorrow I will mail it by post.

Temporary eligibility: You need to provide more information within the next 3 months to keep your coverage.

The question what worries me most of all at the moment is: if I don't pay US tax because I have UK government pension they will charge me back with this $630 a month.

What do you intend to send by post? Your passport with visa stamp enclosed?? Do not do that!

Check out a site called enrollva.org that is for folks in Virginia looking for affordable care advice and coverage.

I will post a copy of the page with my immigration visa. NOT original.

I will do it tomorrow. Thanks for your advise. It looks promising.

If you get a health care tax credit/subsidy you must file a US tax return. Also I would file taxes in both the US and the UK to keep your accounting straight.

Here is a map of where to get assistance with health insurance in Virginia

http://www.coverva.org/app_assistance.cfm

Yes, I will file it here, in the UK they take it out of the pension automatically.

That would be my assumption as well; the OP is now a US permanent resident so her UK travel/medical insurance is now completely void. Thankfully, the OP is working towards getting US medical insurance now, so that's good.

Make sure you claim your UK personal allowance now that you are not resident in the UK.