I have two more years to complete a Ph.D. with a valid I-20, but my Visa expires in August 2013. I want to visit India in June-July 2013. If I come back in July, do I need to apply for F-1 visa (and F-2 visa for my family) extension? Would I have problem in reentry if I have one more month of valid F-1/F-2 visa?
You will need a new visa only if you return after August 2013. Check with your DSO to make sure you have all the appropriate requirements completed.