About to renew my Indian passport and have a few questions

I am currently living in New York and my passport is up for renewal shortly. Here is a (hopefully clear) rundown of my situation:

- My current passport which was issued in Dubai and is a hand-written passport is set to expire in March and I am getting started on the renewal process.
- My current passport does not split my name between first name and last name - My entire name is handwritten on the given name line.
- My H-1B visa, which is valid until August 2015 shows "FNU" as my first name and "John Doe" as my last name.
- My social security card, on the other hand, shows my first name as "John Doe" and my last name as "LNU.
- Because of this, I haven't been able to get a drivers licence in the last few years that I have been here in addition to issues when opening up bank accounts, getting a phone connection, etc.

Since it is time for me to renew my passport, I figure this is the best time to get all of this sorted out. My question is how exactly I would go about doing this.

1. Can I get my passport renewed and the name changed at the same time, i.e., can it be one application? If I have to do it in multiple applications, which one should I do first?
2. I'm assuming my H-1B visa stamped in my old passport will be returned to me attached to new passport and I will not have to get the H-1B visa stamped again but I would appreciate if someone confirmed this.
3. How do I get my name fixed with the SSA? Do I just submit a name change application once I get the new passport?
4. Anything else I should know before I get started with all of this?

I believe these are all my questions for now. Thanks in advance for all your help.