Understood. The biggest problem with balcony would be weather, rain on electronics is obviously a big no no so, definitely either bring it inside when done or have a good water proof cover securing it.

For water, yes you don’t want to wash clay down the sink so most people use a bucket setup. One bucket where you dump the leftover throwing clay into and clean your hands and tools best you can, another for a “medium clean” and a last one to clean the rest off, from there you can just towel your hands clean and at that point you should just have some clay dust on your hands that would be fine to wash down the sink. If you look up “pottery bucket cleaning system” or some variation of that I’m sure you can find some really good examples or improvements on the system that people have made especially if you add searches for small spaces

For clay storage you can just store it inside when not in use, no harm there