Yes. I'm doing it for my house. 100,000L underground storage, planning to supply all the toilets and also to supply the washing machine. Filtered of course. Practical or not it depends, I built a new house so for me it was just digging a hole. If you have a house already, very hard to find a place to put your storage tank and for the plumbing too.

Yeah, that's true. Pumping it with the water pump.

Run it through a filter just like you would do for the government piped water. That's what I did for mine.