Using distilled water as the basic medium is just fine. BUT I would also add to the distilled water an appropriate water conditioner that is related to the type of use that I have in mind for the aquarium. The link below is to one of several online retailers who sell water conditioners. Use the link to see the variety and the types of use that each is for so that you can find the one that is best for your plans on stocking the aquarium.

Here is a link that might be useful: Water conditioners

There have been times and places when bottled water sold as "Distilled Water" was just tap water. I found this out when working in a laboratory where I had water testing equipment and called them on it and they 'fessed up.

Not a good idea IMHO. Animals and plants needs the nutrients that regular water contains. Also distilled water has no buffering capacity. When your fish expel waste the distilled water will have no ability to buffer the buildup of toxins. Your ph will likely spike into being very acidic and everything will die off.

Yes definitely a bad idea. There are also minerals that if not in solution will be drawn out of fish/animals particularly if this is a saltwater aquarium. Best to purchase an RO/DI filter for your water changes.

Scott