Will a one week gap in employement, even when H1 transfer is filed, affect my status? Will it account for unemployed days?

I am assuming you provided accurate information regarding last date of employment, etc to your new employer's immigration attorney. Did they...

Can spouse attend visa stamping for H4 using new Employer's petition approval?

Yes

Separated will affect your citizenship?

Unless the IO allowed you to amend it to be considered as a regular 5-yr LPR filing case.

H1B transferred is approved, but not joining the company at least for 1 month, in between can I visit India for 2 weeks ?

This question will be best answered by the new company's immigration attorney.

I am working on L1B Visa and my H1B is also approved in Jan-2013. My L1B is expiring on July-2013

You will send paperwork of status you are currently maintaining.

Yes

H1 B status pending, travel outside USA, options available?

Every time you travel you should consult with the company's immigration attorney.

I have a U.S Visitor visa can i go to a immigration attorney and help me to work and stay in U.S or its a waste of time ?

On visitor visa you can do neither. If you wish to discuss other prospects to change status, you may want to consult with a competent immigration...

F1 visa married to US citizen, but no I130/I1485 filed. Can I travel home and return on my F1 visa and then file I130/I485?

I don't advise travel in F-1 status when married to USC. Entry may be denied as you have immigrant intent. Best way to proceed is to file I-130/...

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What will happen if i decided i want to cancel my petition I-130 for my immigrant spouse?

You don't have to withdraw the petition just because you had a fight. Talk to an immigration attorney to evaluate the situation and guide you...