If you are currently illegal in this country, then the answers are "no" and "no".

I'm legal- student

As a spouse of a permanent resident you may get a green card. However, the waiting time for this immigration category is about 2 and a half years now. During that waiting time you will have to obey the regulattions of your current non-immigrant visa/status.

Can I get any permission to visit my country?

If your student visa is a multiple-entry visa, then you do not need any permissions to travel internationally and to return back to the United States. Your legal status here (a student) will not change after your spouse will file an immigration petition on your behalf,

I have student status, can I get white passport or something to see family

Are you a citizen of any country? If so, then you should have a valid passport issued by that country. Do you have a student visa in your passport? How did you actually enter the united states? As a student? Or you got the student status while ialready being in the usa, and you do not have a student visa in your passport?

The "white passport" is not a passport. It is called Refugee Travel Document. It can be issued by american autorities for refugees and for stateless persons. If you are not a refugee, and have a citizenship of any country, than you should travel internationally using a passport issued by the country of your citizenship.

I have status- got it here

Would like to see my parents in Ukraine, I am citizen of Ukraine. Looking for chances to go there

You can leave the United States for Ukraine at any time using your ukrainian passport. However, in order to return back to the US, you will need to obtain a student visa in your ukrainian passport from american embassy in Kiev. That is not guaranteed. There is a possibility, that the american embassy would decline your visa application (for any reason). Then, you will get stuck in Ukraine and will not be able to come back to the United States to continue your education here,

In your case It would make more sense to invite your parents to visit you here in the US.

Thank you, but is there any chances to speed up process with my green card after marriage?

someone told me about some imergency travel permission, that i can try to get, but basically i am asking about my chance to get opportunity to see my country after marrige with green card holder, or ot is better to wait untill he will get citizentship, but kind of will take forever

There is no way to speed up your green card process after your marriage with a permanent resident. Currently, it takes 2.5 years. Unless your spouse will become a citizen. Then you will be able to get your green card almost immediately (in a few months).

You do not have any restrictions to leave the United States - you can do that at any time. The possible problem - how to come back here. As I said - if you would have a multiple-entry student visa in your ukrainian passport, you wouldn't have to worry about anything.

Marriage with a green card holder does not give you any immediate rights to stay in the US or to travel to USA (until your immigration visa number will become available - in 2.5 years). Until that time, you must have a valid non-immigrant visa (student, work, etc.), in order to return back to the US.

Anonim, chitatel tebe srazu otvetil, chto povtoryaesh vopros opyat i opyat? Za citizena viidesh, poluchish green card cherez kakoe-to vremya, za green card holder-no.

>>to see my country after marrige with green card holder,
Читатель Вам пояснил что брак с грин кард холдэр НЕ дает никакого статуса сразу. Если Вы заключите брак и подадите петицию то если Вы покинете страну Вас не впустят обратно даже если есть действительная неиммиграционная виза: ибо Вы задекларировали иммиграционное намерение вступив в брак с грин кард холдэром. Вам скажут ждать за пределами страны своей очереди и иммиграционной визы. Потому советую не покидать страну пока не получите временную грин карту.
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