What is H-4 Visa processing requirement after company/institute change for H1B visa holder?

As long as you are maintaining valid H-1B status your spouse will retain H4 through her expiry date

I-130 for Parent , US Citizen

If you are a US citizen petitioning for your mother there are no derivative. If the child is classifiable as your sibling you may petition for your...

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When your daughter becomes a US citizen she may petition for you to reisedein the US

I have expired H1 visa (2013) & my sister (USC) filled I-130 visa under F4 in 2014, my employer applying for H1 transfer

The H-1B has dual intent and an I130 filing has no impact. Always answer truthfully

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Affidavit of support part 5

2 for you for joint the sponsor spouse children dependents and any other dependents

Can H4 travel to USA while H1B is still in India.

Yes if he first obtains the H4 from the US consulate.

Filed I-751 jointly on October 25th 2013 as seperated. Case is transfered to field office Tampa in the month of September2014.

Sometimes files don't get tracked at CIS sometimes there is an issue.

Can i apply for F1 visa through a U.S embassy while i m having a U-visa pending case ?

It is possible but it is also possible the consulate will not grant the F visa.

Naturalization Interview was on 10/23/2014 with approval

Normal. It usually takes about a month or more for the oath ceremony.

False accused, went to trial but not convicted.

You need a certified copy of the disposition. You may also want to obtain a copy of the police report (certified)