Tropit, I just use microfiber cloths and plain water to clean windows and mirrors. A wet cloth to wipe/rub clean and a dry one to dry the glass. Save that vodka for special times - which these days comes daily!
I also use baking soda and white vinegar to clean sinks, showers, and tubs. Sprinkle the dry baking soda over the surface and spray with vinegar (I keep in a garden type spray bottle) or just splash it around, it will foam up. I let it sit a bit and scrub with a brush or cloth depending on how dirty and my mood
.
I finally had to order hand soap from Amazon as I couldn't find any in the stores here. Your solution with dish soap sounds perfect.