Google Loon or whatever they called the stratospheric balloons carrying solar powered cell/wifi base stations that made their way around the earth with the Jetstream or w/e used a bladder in the balloon that was inflated/deflated with ambient air. Similar to a ship taking/releasing ballast water in ballast tanks.

Rigid airships still have flexible gas bags (cells) inside. They just have a rigid hull around them.

Yes, although a better way of saying it is that it is not the helium which has lifting power, it is the balloon. A balloon has lifting power equal to the weight of the air displaced by the volume of the balloon. From this, you must subtract the weight of the balloon and its contents. Helium is one of the few materials that allows you to wind up with a positive net lift.

(Also, for this to work, 1kg of helium would occupy a balloon much larger than 10cm^3).

The helium is only to keep the baloon of given volume from collapsing.

Yes, like how a 1kg 10cm^3 block of wood will have more buoyancy in water than a 1kg 5cm^3 block.

Bouyancy “is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid.”

So compressing your lifting gas reduces the amount of air being displaced by its presence, reducing the buoyancy.

Yes - the latter is more dense by a factor of 8 (2^3) and thus has less lifting power.

To take an actual real example:

Air has a weight of 1.222 kilograms/m^3 (dry, clean, standard pressure) Helium has a weight of about 0.167 kg/m^3.

That means that 1m^3 of helium lifts about 1kg. If you now compress that helium by a factor of 10, then 1m^3 of compressed helium would weigh 1.67kg - more than the sourrounding air and provide negative lift.

edit: get your unit and orders of magnitude right. :sigh:

Lifting power is defined by the mass of displaced medium minus the mass of the displacing medium. Change your units from cubic centimetres to cubic metres and the answer is "yes".