What is this balloon doing in this clean room and what is the proper name for the "stand" (white & blue) that is holding the satellite?
The balloon is used to support parts of the spacecraft that can't hold their own weight in 1 g - booms, appendages, etc.
As you can see from this cropped photo (from here), there is no hose to allow flowing extra gas into the balloon. It is simply connected to the object it supports by a tether.
The stand is called a "positioner" if it allows the spacecraft to be held at multiple angles. But often just referred to as "fixture" or "stand".
A 3-axis positioner can also be used. This is an elaborate fixture that holds the spacecraft at multiple angles to measure all mass properties (CG in 3 axes, MOI in 3 axes, and POI in 3 planes). It allows calculation of product of inertia based on moment of inertia measurement, so the entire inertia tensor can be derived with the use of a KSR instrument. The spacecraft positioner also minimizes handling of the spacecraft. The spacecraft is mounted in a vertical orientation; the positioner rotates the spacecraft to the various measurement positions and brings the spacecraft back to vertical for easy dismounting.
More, and examples here
Having looked at the various ISAC facilities, I suspect that is just an adjustable stand in one of the clean rooms.
Compare to this image search result for 'ISAC clean room':
The stand is adjustable to give easy access to all areas of the satellite without having to use ladders (which can fall over and damage the satellite).
Example, this is a vibration test system at ISAC:
As for the balloon, I haven't found a reference. I suspect it's used to capture overflow helium during filling of the helium tanks in a spacecraft.