A/C - Evaporator Coil Replacement
 

I have a home warranty. My A/C unit broke down last week. It was
turning on, but no cold air coming out of the vents. The first time,
the A/C technician came byb, refilled the freon and the it worked fine
just for a day and the problem resurfaced. The second technician came
by and told me the evaporator coil needed to be replaced - He went up
in the attic and I heard a beep. I assume he did some kind of a freon
leak test. I checked both the A/C units outside and the A/C unit
working fine had a pipe that was cold to touch when it was on and the
one that was broken did not have the same pipe cold to the touch when
it was on.

The home warranty company called me that certain items were not covered
and my part of the bill was $350. Is this amount look good and the
diagnosis the right one.
Should I be asking some additional questions here and make sure that
all that needs (anything extra) to be replaced will be replaced?

Thanks in advance for all who took time to reply to this.

Vasu