In my case, I taught at school that was included in the TCLI Directory only during my first year of teaching. Would the rest of my teaching years be counted towards the 5 years to qualify for the teacher loan forgiveness?
Yes, don't worry, the rest of your teaching years on that school will be counted as well.
I'd also like to know on what do I need to do if I'm ready to apply for the unpaid refund discharge?
Then you must complete the Loan Discharge Application: Unpaid Refund and send the completed form to your loan servicer.