Congratulations on completing the visa process! Your wife is now a Permanent Resident. Great tips on a more conservative approach to documents for Mumbai; I have heard they are their own world there!
I recommend that everyone always keep a photocopy of EVERYTHING they dubmit to USCIS or a Consulate. You may need them later on.
Regarding your questions... The endorsed visa is your wife's temporary (one year) evidence of her PR status. It is an equal substitute for her Green Card, which is being mailed to her. As stated many times, she has now applied for a SSN. If three weeks pass an no SS card arrives, go to your local SSA office.
You do not need to register your marriage in the US; you are legally married as far as anyone here is concerned.
From the DCF Guide:
5- The foreign spouse enters the US, and at the port of entry will have their MRIV endorsed with a stamp. That is now proof of the immigrant’s new status: Permanent Resident. It is adequate evidence for most purposes and is equal to the I-551card that will be mailed to them, also known as the Green Card.
The foreign spouse receives immediate work and travel authorization from the “green card stamp”, and will only need their social security card before starting to work. You may have already applied for this on the visa application DS-230 II. If you have applied for the Social Security number via the visa application, your SS Card s mailed to you separately within a month. Your Green Card will be mailed to you in the same time frame.If you haven’t received anything within a month, it’s time for follow up.
Note: If you have been married for less than 2 years when you enter the US, your Permanent Resident status has “conditions”. A CR-1 PR is no less a PR than anyone else, but they do have an additional step to take 2 years after they enter the US. Please see the Guides for Removal of Conditions (form I-751).
The visa resulting from a DCF case is the same Immigrant Visa that one would get by filing I-130 in the US: CR-1 or IR-1.
I recommend the following reads to anyone who is becoming a Permanent Resident, so you can better understand your rights and responsibilities.
Now That You Are A Permanent Resident
http://uscis.gov/graphics/howdoi/PermRes.htm How Do I Remove the Conditions on Permanent Residence Based on Marriage?
http://uscis.gov/graphics/howdoi/remcond.htmWelcome to the United States:
A Guide for New Immigrants
http://uscis.gov/graphics/citizenship/imm_guide.htmm