One month of satisfactory departure.

What are my chances on getting Dad green card approved after abandonment caused by leaving country for 6 days ?

Processing times are on the VIS website. Denial for lack of prosecution (abandonment) is not an issue in of itsel.

H1B new visa or transfer possible with existing acknowledgment number

The employer is required to pay the prevailing wage as indicated on the petition. If you are not employed H1B status ends.

I have h1b approved H1b for april 2015. If i join any other company can i transfer h1b and will it be valid?

You need the have H1b status to change employers, Speak with your employers immigration attorney.

I am on h4 now. I have approved h1b. What is the process of conversion of h1b from h4?

A change of status could have been requested concurrent with the H1b status. If not file one now.

What are my chances of getting a student visa if I have a I-130 petition filed through my sibling?

You may have more difficulty than someone similarly situated that does not have an immigrant visa petition pending

I have a question.

You may file a petition for her now and if you are eligible to become a US citizen before her priority date is reached, you may 'upgrade' the...

I-751 Interview

You can try contacting CIS and explain the situation and ask for another appointment date.

Does EAD obtained through TPS interfere with getting another EAD in the future?

As my colleagues have noted the TPS EAD does not impact the I-140/I485 process.

Affidavit of support sponsor qualification

Depends on the number of persons the sponsor supports for the amount required see http://www.uscis.gov/sites/default/files/files/form/i-864p.pdf