Hello radishgal, with my houseplants, so far I have not seen the need to shower them. But most tropical plants will not mind a good shower, as long as you do it early in the day and allow excess water to drain off properly. Run your ceiling fans or open your windows to help with drying out and air circulation.
You got a good collection of plants, just make sure you use containers with drainage holes so excess water and salts will be flushed out properly during watering. With succulents especially, water has to drain out, otherwise you risk root rot. It also helps to add more pumice or perlite to your soil to really make it well draining and allow good airflow at root zone.
If for some reason your plants shows distress later, best to delay fertilizer application, it will not solve its problems, and may just cause further fertilizer burn on the leaves and roots.
And if I may make a slight comment too on the combination of succulents in your container, the Sansevieria ( the one that is twisted in a ponytail) is good for indoor growing being a low light plant, but the other two is best grown with more light, nearest to your south facing window or outdoors if possible. But it is your preference and choice, just pointing out those plants growing needs.
As to the water used, I just use tap water for my plants. I only use distilled water for my carnivorous plants.
Have fun on your gardening!