No.

Want to go back to employer A after joining employer B for a week on H1B!

Yes, you may return to the previous employer as long as the petition was not revoked and you have been maintaining status.

Verifying trips outside U.S

USCIS has records of most LPR entries and exits, which are relevant in determining Naturalization eligibility.

Which law is the one which prevent a person with a domestic violence case to become a united states citizen?

A person convicted of a domestic violence fine may be deportable from the US, depending on the date and nature of the conviction. USCIS will not...

I AM CURRENTLY IN USA WITH B1 B 2 TOURISTIC VISA*VALID*...HOW CAN I GET H2B VISA TO BE ABLE TO WORK.THANKS

You must have an employer willing to sponsor you for a change of status.

I am filing the I-130 the end of this week for my husband. How does my mother cosign.

She will be a joint sponsor on the affidavit of support.

Will i need to take another physical when i get a response from my 1-601 form

It is not clear why you are applying for an I-601. Please provide more information.

H1 is approved for Employer A,from Oct-01-13,but planing to shift to employer B.

You may be deemed out of status if you do not work for employer A, which would make you ineligible for a change of employer/extension of status.

Spouse wants an annulment less than a month into the marriage.

Potentially. if the family court enters an order identifying fraud as the grounds for the annulment.

Approval i360

The interview is to adjudicate the I-485, Application for Adjustment of Status.