I realize you are blinded by hope here...I was too after the supposed "special moments" of sex with my WAW...but it is jading your thinking my friend. Reading too deep into it desperately seeking any glimmer of hope that she's falling back in love with you.
Hope is great, but I'm just going to say, I don't like the smell of this whole green card/let's stay married idea. Sounds to me, like others said about her using you for the sex, that this is just another benefit she can get from you without R.
Her emotions and feelings and love for you should be the only thing that makes her want to stay married...this is more like an "I want to still walk out but staying married gives me sex and citizenship. Hate to say it, I think she's using you at this point...

Having said that, I pray I am dead wrong and this works out for you. Jusr please protect yourself.

ME: 43 W:44
M 13 years on 5-5-01
T 18 years
BD 4/27/14
D papers served 5/5/14 (how appropriate a date)
WAW moved out 5/12/14
Papers filed 6/27/14
Divorce granted 07/17/14
Our marriage ends 11/17/14