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Hello Rajiv Ji,
Thanks for your time and responses (over the email). I have below questions.

1) I am an EB-2, with Priority date Jun-2008. Applied i-485 in Jan-2012. Cut-off date became current in July-2014. Through congressperson / infopass found that my application is in background checks.
1.a) I have given fingerprints 2.5 years ago and background checks are not cleared yet. so what are my options in expediting it?
1.b) My worry is the checks may not be cleared before next time dates become current, and I may be in the same situation again.
1.b) Can I use Writ of Mandamus? Does my case (485 pending for 2.5 years, current for 2.5 months, but background checks are not completed yet) have enough reasons to claim "unreasonable delay"?

2) I am using my EAD. My labor says "Senior Analyst" as my job title.
2.a) Can I accept a promotion with a director/managerial job title ?
2.b) or does it cause a problem / RFE in future? Duties are more or less similar and work on same software technology, but will have few direct reports and need to manage projects.

3) Can I switch to H1-B as a safe measure?
3.a) Does switching mean I am abandoning my GC?
3.b) Do I need to go out of the country for stamping or can I continue to work without going out?
3.b) what are the risks involved?

My sister filed petition for me last year maybe I-130. I am an Indian and my wife is Italian, I am in California nowadays since last week. Can we stay here permanently under I-485 or AOS whatever?