My refrigerator and all those I have seen on the market have freezer compartments where ice trays containing anything you could desire can be accommodated. There are no buttons to be pushed but I have plenty of buttons on other appliances that fulfill any button pushing impulses I may develop.

I am not too sure about this one. You most certainly spend a lot time thinking about the fridge. I think, with a design as such you would find that many of your flavored ices would change in taste as they aged in the fridge. I am not too sure you would find much of a market.

Doable. Just use smaller ice syrup or juice compartments.

this would actually be fairly easy, as ice makers have their water valve outside the insulation, so that there is no water sitting in tubing inside to freeze. so all you would have to do is add small tanks on top of the freezer, and have a solinoid controlled valve on the back of the freezer to control which line is allowed to flow into the ice maker. a standard ice maker could potentially make a whole variety of ice. though i do agree that it is probably far simpler to just buy the plastic trays and make the ice the old way, rather than setting up containers, valves, and control chips, or if one were thinking of producing this system, i'm guessing you would have to sell it for at least $200, even if it was a piece of crap, so why would anyone buy this instead of $20 of ice cube trays