If your Father no longer has a valid visa to reenter the U.S., he must first obtain a valid visa to return. However, there is no requirement that he obtain a new Visa just because he sought an extension in the U.S. notwithstanding the outcome of that extension.
The following link provides the details of Visitor's visa. http://travel.state.gov/content/visas/en/visit/visitor.html
As long as your parents have a genuine need to visit and remain visitors, there is no limit on the number of trips they are allowed to make. However, care must be taken to document that frequent visits are not a way of remaining in the U.S. permanently.
Your daughter is not technically a dependent and may not benefit from your Green Card. Be this as it may, she may be able to travel to the U.S. in a nonimmigrant classification as a dependent if it can be shown that she is dependent on you entirely for care and support. The application process [...]
The Service requires you to file a Form AR-11. This form is available on the Service website at www.uscis.gov
This is a broad question. Let us address it in a logical way: Nonimmigrants: Extension of Status situations: An individual can travel when the INS is processing a petition for extension of status, provided the individual has an unexpired visa to travel and return to the United States. Change of Status situations: Travel is prohibited [...]
In SEVP's OPT 2010 Policy Guidance, Section 7.2.1 (p. 17-18) states, in part: “Unpaid employment. A student may work as a volunteer or unpaid intern, where this practice does not violate any labor laws. The work must be at least 20 hours per week for a student on post-completion OPT. A student must be able [...]
USCIS FAQ on how to use the Premium Processing Service
Your questions are case specific and complex. We suggest you schedule an appointment to discuss your situation. Be this as it may, a child born to a U.S. Citizen is automatically accorded citizenship and your child will benefit by this automatic child citizenship provision. The Attorney recommends that you continue the process towards your naturalization [...]
Your question pertains to Naturalization when married to a U.S. Citizen. In your case, although you have been married for three years, you have only been a permanent resident for less than two years. You would have to wait until 2 years and 9 months from the time you became a permanent resident to apply [...]