Here's my 2¢
1. Applying for jobs in the US might be more difficult if Vivek does not have his green card yet - but it's not impossible! I would think that a company who doesn't necessarily want to sponsor his green card might be interested in him if they know he will get a spousal green card (only a matter of time).
You can look into the different visas available - the K1 is a fiance visa, which means you apply before you are married (while your "fiance" is still in their home country). They eventually get the visa and can travel to the USA - once they arrive, you have 90 days to get married and apply to "adjust their status" which means they get a work permit and then a green card. The other option is to marry first and then apply for the spousal visa (to travel to the USA) a K3 visa. This is similar to the process of the K1 - except you are already married and you have a set amount of time to apply for your adjustment of status/green card.
2. Becoming a citizen: "Live in the U.S. for at least 5 years as a permanent resident (or 3 years if married to and living with a U.S.citizen). Be present in the U.S. for at least 30 months out of the past 5 years (or 18 months out of the past 3 years if married to and living with a U.S. citizen). Live within a state or district for at
least 3 months before you apply." (taken from here: http://www.uscis.gov/files/nativedocuments/M-618.pdf
I have a copy of this saved on my computer!) You'll want to refer to this website a lot: http://www.uscis.gov/portal/site/uscis
3. Yes, and Indian who becomes a US citizen has to give up their citizenship - but there are options which are **not quite** but similar to dual citizenship (PIO & OCI) - check out my blog post: http://indianties.blogspot.com/2008/09/making-sense-of-indian-visas-for.html
4. Um... I've tried to block out the fees!
lol Actually, I'm not sure anymore because they keep changing them! And it depends on which route you go. But just about every form that you have to file has a substantial fee attached to it. We are applying soon for a new (10 year) green card (the original 2-year one is expiring soon) - and I think it's around 500-600 dollars. Check the USCIS website (above) for exact amounts.
5. I've known several Indian grad students who have applied for jobs after finishing school - but I also heard that there is a certain length of time that they have to find a job before their status expires. So I guess it could be a bit of a risk to go that route...
We went for a K3 visa - a spousal visa. We were already married at the time we wanted to both live and work in the US (we lived out of the US for our first year of marriage). So my husband entered the USA on the K3 visa and had a few months to apply for the green card. You can live and work in the US until your green card is granted (or denied!). Our green-card interview was only a couple of weeks before our 2nd anniversary. So because we hadn't been married for 2 yrs at the time of the interview - we have to now re-apply for the 10 year green card (and prove that we are still married!). The original green card was good for 2 years from the date of issue.
Hope I've answered a few of your questions - the thing that helped us the most was getting a consultation with an immigration lawyer. They usually give you a free consultation and help you know what forms/visas you should apply for. Then you can choose to use their services to proceed or go for it alone - we used the lawyer the first time - but I think we'll file the new green card papers on our own this time around.
I'm sure some others have experiences/advice they can add as well....