Each mortgage lender has different requirements, one of which is a specific credit score. If you have a recent bankruptcy, you likely cannot meet that requirements.
May be difficult to finance your home under Chapter 13. Chapter 13 is a reorganization of debt so other creditors on your old debt will claim first before mortgage company.
Yes, but you must make every payment to your current lender and trustee on time and in full. Your trustee will make the final decision if you can refinance.