Yes, you can use the current appraised value of your house to help eliminate mortgage insurance on a Conventional mortgage. However, you will most likely need 25% equity vs the normal 20% for the mortgage servicer to approve the elimination.
Maybe. Paying off your student loans might help reduce your debt to income ratio allowing you to qualify for a higher loan amount. However, paying off installemnt debts like student loans and car loans might lower your credit score.
It depends upon when your hard credit report was pulled. Most lenders require a mortgage to close within 120 days of the credit report being pulled for that report to be used.