The brakes on my daughter's 1997 Pontiac Sunfire hiss or sound like air when she presses them. The fluid doesn't seem to have leaked yet.

sounds maybe booster is diaphram is bad

Well its just like the brake system, the fluid has to be going somewhere.
Is it leaking into the bellhousing around the clutch ?

the leather inside master cylinder is leaking. Buy a kit or a rebuilt from parts store.

Sounds like the vacuum booster.Check all hoses to and from it

The ground checks out? Which ground did you test?

The clutch system is hydraulic just like your brakes are. You have a slave cylinder and a master cylinder. You must have a leak somewhere, and will have to see what part it is, or have it looked at. Once replaced, the system needs to be bled of air just like brakes do.

well, you don't really hear air when you press the brake pedal. You might hear hydraulic fluid going through the valves in the master cylinder, that sounds like air flowing through a vent. But, I assure you, it is not air.

One can press and pump on the pedal when the car is off and hear the 'rush' of fluid which sounds kind of like air rushing out of an inner tube.

It's a common mistake to believe a rush of air is being heard when pushing on the brake pedal.

I would suspect there is either a crack in your brake line. the fluid has to go somewhere if youre having to refill the reservior. Maybe they didnt bleed them after the work was done, and had an air bubble and when you applied pressure is blew out a fitting. needs to be checked out though for sure!

it sounds like the immobilizer is faulty. this will shut off the electrical feed to the starter motor. you will need to take it to a garage to get this fixed.

hope this helps.

A vacuum leak could be the problem.A visual inspection of the vacuum hoses would be in order.If you hear a hiss sound when at idle you have a bad vacuum hose/line.