American Home warranty- Duct work

Bought new house recently and saw our heating is uneven in some rooms. We first called insulation folks who said that our duct work is old 30+ years at least and is leaking. Sheet metal duct work with only screws holding them together. I saw that my home warranty covers duct work and I planning on calling them to come and check so that any repair work can be done by them I.e fix leaks.

My question is if they will do any kind of fixes for duct work . Insulation is black in some areas which are signs of leaks.

How do I best use the home warranty service call?And what should I be careful of?