You use the vacuum cleaner according to the instructions provided on the user manual.
If the vacuum cleaner is powered by electricity this is used to turn the electric motor which is needed to create the suction or vacuum. That motor either has permanent magnets inside it, or the current passes through many "turns" of wire to create magnets when you switch the cleaner on. Early experiment in electricity showed that if a wire is moved in a magnetic field some current is created. Similarly, if a magnet is moved near to a wire the same result occurs. So, yes the cleaner does need a magnet.
No At least, not unless it happens to have a very large magnet in it for some reason.
electrical
Use carb cleaner or brake cleaner.
Use an antique hand pumped vacuum cleaner (they existed before the electric ones).
Some kind of magnet or magnetic field is necessary for a motor to operate. Alternating current vacuum cleaners (that plug into the wall) have motors with electromagnets. Direct current vacuum cleaners (that plug into the car's cigarette lighter socket) have motors with permanent magnets.
That depends on the distance to the vacuum cleaner. The closer, the louder.
universal motor
Vacuum cleaner
In the motor used to turn the fan that creates the suction, though you might find magnets as closures too.
Yes, we are vacuum cleaners of the vacuum cleaners, which are the floor cleaners