If you run all the drives 24/7 I would guess you are looking at somewhere around 400W assuming a power sipping minipc as the host. This can be extremely optimized if you intelligently spin down disks when idle, probably down to >50W average.

Cost will depend on your electricity contract, but will propbably not be a thing that would stop you if you want to do this.

From "negligible" to "I have another house inside my house" levels, depending on your hardware.

A close friend of mine runs a single beefy server at home, which is currently ~35% of his monthly bill if I'm not making mental-math mistakes.