1 Extension. Yes you can apply for an extension.
2 Adjustment to Green Card. It is possible but must be done carefully. Filing may raise doubts about the visitor's intention to remain temporarily in the U.S. at the time of entry. This is especially true if the filing is submitted soon after entry. If it is determined that the visitor entered without the requisite intent to leave after a temporary stay, the visitor may be accused of fraud and/or misrepresentation in entering the U.S. This can have dire consequences including permanent denial of entry into the U.S.
3 Before you file anything, contact an immigration attorney to assist you. You can find one in your area at the Find a Lawyer section of this website. Good Luck.
Yes, you can do both but not in parallel. In the context of the extension of status, he might be denied for the reasons you outlined. In the context of adjustment of status you might run into a preconceived intent issue. Hire an immigration lawyer.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
Hi -- your father can apply for the B-1/B-2 extension. Or, you can also petition for status for your father, and at the same time he can file for the adjustment of status, since your are a US citizen and your father is considered your immediate relative for which a visa is immediately available (so to speak, since there's still processing time).