You probably should ask admissions at two or three universities that you are interested in and see what they say.
I would expect that you need to obtain a transcript from your school in the Ukraine. If it is completely different from the transcript from a US school that is okay. Admissions will be able to tell you whether they will take the transcript as is, or if some form of translation or additional information is needed. Also, you can describe what you already have and admissions can tell you whether it is all that they need. As @collegemom3717 said, many students manage to apply to schools in the US from high schools outside the US. We have done the opposite – applying to universities outside the US from high schools inside the US, and did not have any problems.
Universities in the US should know how to interpret the 12 point system from your high school in the Ukraine.
High school transcripts normally include grades from all four years of high school.
A “green card” is of course an informal term for a permanent resident visa. This means that you are considered the same as a US citizen for the purpose of university (and for many other purposes).