Will I need to obtain a medical examination report?

If you are in refugee status when you apply, you must submit a completed Vaccination Supplement Form only (Supplement to Form I-693, Medical Examination of Aliens Seeking Adjustment of Status).
If you are an asylee when you apply, you must submit a completed I-693 in addition to the Vaccination Supplement Form.
Should I apply for employment authorization with the application for permanent resident status?
Even though you can apply for employment authorization when you apply for permanent resident status, it may not be necessary to do so. Refugees and asylees are authorized to work as soon as they are admitted or granted such status and can apply for an Employment Authorization Document (EAD).