Mostly no but I've often made coffee, thrown it in a mug then covered mug with foil & put in a fridge to chill out. Done it a few times the night before so can just have a chilled coffee drink in the summer instead of something hot in the morning. Considering how quickly the small coffee makers make coffee, I'd still go with in the future of making it right before you're drinking it & just wait the 15 min (or less if using the microwave for heating the water) to make a much tastier coffee.
Always. Coffee takes a lot longer to spoil than you'd think (or maybe a lot less time, I don't know you).
I've had four- and five-day-old coffee many times, but day-old usually tastes better than fresh.
But I take it black; if I put anything in it I would never let it sit. Milk's one of the most volatile foods and sugar just encourages bacteria.
6 to 8 hours is about the limit for me, and that's obviously if it's untouched (no cream or sugar) in the carafe or in an insulated container like a Zojirushi. I certainly wouldn't drink anything that had sat around with milk in it for that long. Old coffee is pretty awful, but sometimes I'm more interested in being alert than having happy taste buds.