It would be great if the balancer not only had the option to set priority/no priority, but also to assign a number so the balancer could define the exact order. Similarly, storage outputs have a global setting to halt transport to the conveyor belt/pipe at a specific size. However, this setting is the same for all outputs. It would be nice if they could be defined separately. For example, supplying a gas station with fuel, but if the tank is almost full, the excess will be redirected to a second output leading to the burner. Another idea is fuel mixing. A boiler (gas) can be fueled with any fluid, but only one at a time. I think burning a mixture of heavy oil, light oil, and naphtha in it should also work. Alternatively, adding logic, for example, to the balancer, would work. Draw from this input if the nearest supplying storage has more than X.

Or maybe it's possible to do all this, but I haven't figured it out?

All of these are great imo. You can do workarounds for all of your problems currently:

1. Balancer priority - you can have as many priorities as you want, but you have to add an extra balancer. For example, first balancer takes first priority out to a fuel station, second priority goes into another balancer that can sort by priorities again (e.g. a fuel storage and then a burner). But it is more cumbersome than necessary
2. The outputs from storages halting transports separately - I thought this to be a great addition as well. You can, however, do this with a balancer before the storage - priority one to a fuel station, pripriority two to a storage. Then priority three to a burner if you want (add an extra balancer).
3. The boilers can be "sushi-fed". Add a connector to the fuel input. Then connect up to 3 maximum fuel pipes to the connector directly (usually heavy oil, light oil, naptha in the context of a refinery, for example. YMMV). Also, this can be solved with a balancer, too. Connect a balancer before the boiler and connect that balancer to the fuel input with a short pipe (short pipe so it doesn't hold more fuel than the boiler itself can store internally before "clogging"). Use priorities on the balancer...or not. Your choice. Personally, I use this solution for farm fertilizers, not boilers, but it should work just fine.

All in all, while there are workarounds which aren't too complicated, you are right. This game ultimately needs some sort of very customizable circuit system (a la Factorio) so that everyone can get creative with solving these problems.

Thanks for reply. Workarounds are OK. I will try. But you know... I am an engineer. I hate workarounds ;)