1. Have you ever encountered a situation where you needed something cooled right away? (i.e. food, drink, medication, etc.)
No, other than ice cubes for a drink / champagne bucket.
2. If my teammate and I made an appliance the size of a microwave that chilled and/or froze an item faster than a refrigerator/freezer, would you buy it? What would you use it for and how would you feel?
No.
However, perhaps I would be more likely to buy a microwave if it also came with a "chill/freeze" option, so that it did not take up more room in the kitchen, especially if it did not add much to the price.
3. This idea would basically be the opposite of a microwave, and with that in mind, do you feel that this would be a necessity or a novelty?
Clearly not a necessity in the domestic market as there is no "long felt need". There may be some specialist markets (e.g. professional kitchens, operating theatres, small scale catering outlets, etc.)