-Is that 1L developer working solution thrown away after each session or is it reused?
-What would its shelf life be?
No! The shelf life of the used working solution seems to be practically unlimited. No problem after many years. Also, you can do enormous amount of prints with just one liter.
The blix probably has a little bit less, but anyhow, I've been using blix more than a year old without any problems. But that is from Kodak. Tetenal's blix was always either dead on arrival, or went bad in just few weeks. This seems, however, to be a different (professional) product so maybe this is good.
You can try it at room temperature, develop for 2-3 minutes, and you can omit the starter.