The warranty is 5 years/60k miles. If the car is still within that period,
then the water pump, coil, radiator cap, and whatever gasket you're talking
about should be covered.
As for needing all those repairs for the car to run, I doubt it. Ask the
repair facility specifically why each item is needed, and the detriment
for not doing it. The idea that eight things went bad all at the same
exact moment to cause your car to not run is preposterous. If they tell
you you need all these items in order to be able to drive away from their
facility, have your car towed to an honest repair facility.