Each has merits, but in our evaluation, if you are able to overcome the aircraft design challenges, fixed-wing offers a far more capable platform. The stratosphere has winds that can exceed 100km/h. With balloons, station-keeping is an enormous challenge. We spoke to a lot of people in the Google Loon project, and ultimately this became a defining problem for them. Airships/dirigibles help a bit, but still have to drift in strong winds - beyond that, they also become extremely large and expensive to work with.

What fraction of the power budget do you think will remain for non-propulsion?

The main thing I learned working on Loon is that satellites stay up just fine, and aren't affected by the wind.

Probably for control reasons. You can send balloons up to that altitude, but they'll go where the wind takes them.

I'd guess because it's less prone to get interfered with by wind, more easily controllable, and can stay up longer if battery power lasts overnight.

I too would like to see more autonomous hydrogen balloons flying. Even on tethers to get height cheaper than a tower.

I'm not well-read on the technology involved. Is it possible (feasible?) to use a high altitude balloon to get a plane to altitude?

You could either detach from the balloon, or use spare solar power to deflate the balloon in case you need it again. Maybe the balloon could help maintain altitude at night.

Perhaps not as high altitude as the stratosphere, but the US was experimenting with deployment and 'landing' of fixed wing aircraft from airships in the 1930s. https://en.wikipedia.org/wiki/USS_Akron

They also tried building aircraft carriers out of ice in the 40s. Doesn't mean it was a good idea.