It is a matter of opinions what decor goes well with the fan. Some of the decor that can look nice with the fan can be fountains with falling water or mirrors.
Because hot air goes up, in a house ask of the hot air is going to accumulate at the ceiling and when the ceiling fans go backward in the winter its to push the hot air down so that hot air is moving around the house keeping us warm in winter.
If what you are referring, is the blue Neutral wire in the UK/Ireland, it eventually connects to ground or earth potential at some point on its way to the power station. It is usually at or near zero volts potential but may not always be so.
Yes, a light bulb is considered a fixture if it is permanently attached to a structure like a ceiling or a wall. Fixtures are typically considered part of the property and are not usually removed when the property is sold or transferred.
I've never heard of a DC ceiling fan, but.. AC-Alternating current. Electricity flows through a circuit in one direction, then changes direction and goes back the other way. This happens 60 times per second in the US. (60Hz) The US power distribution system is AC. DC-Direct Current. Electricity flows through a circuit in only one direction continuously. Batteries powering a flashlight, for example, are DC. Well, all batteries are DC. Like I said, I've never heard of a DC ceiling fan, but the DC fan's motor is designed to run on DC (such as batteries) only, and the AC fan motor is designed to run on AC only. I have heard however of a solar powered attic ventilator, which would be a DC fan. If there is a DC ceiling fan, however, keep in mind it needs a power source, and you won't be able to hook it up to the electrical box in the ceiling. That box is AC. The power source for a DC ceiling fan is likely replaceable batteries or solar cells, neither of which will make for a very robust fan.
In the absence of better information and without testing it I would say yes, connect the black to the yellow. When you make decisions like this, be very watchful (as you should always be) when turning on the power so you can quickly turn it off if something goes wrong.
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