I would be interested in knowing if step down transformers can be installed in the attic where the fan is to be installed.

I will recommend you to put the transformer all the way down in the basement and sending the output wires up, having a heat and ignition source in your attic is not the best idea if your house is made of wood, most basement are completely made of concrete so if the transformer catches fire it would be less worse. If you don't have a basement and your only option is the attic you will need to install the transformer inside an electrical steel box and putting an insulation plate for keep the heat away from the wood.

If there's no ventilation, the heat of the transformer will turn the wood that is touching into gas, that will accumulate and might explode.

The motors usually need higher currents for startup (when they tend to loose the magnetic "grip") but then let the current to drop when it is at speed, so the ballast isn't good idea.

The ballast is chosen according to run current. It will reduce starting torque, so the fan will take longer to get to speed. Is this a problem ?

(If the motor fails to start at all, the current is still limited by the ballast to something not that much higher than nominal, so i expect it would not overheat by huge extent)

I will recommend you to put the transformer all the way down in the basement and sending the output wires up, having a heat and ignition source in your attic is not the best idea if your house is made of wood, most basement are completely made of concrete so if the transformer catches fire it would be less worse. If you don't have a basement and your only option is the attic you will need to install the transformer inside an electrical steel box and putting an insulation plate for keep the heat away from the wood.

If there's no ventilation, the heat of the transformer will turn the wood that is touching into gas, that will accumulate and might explode.

The transformer will decompose only the area of wood it touches directly. This won't produce enough gas to get to any combustible levels when diffused over the attic volume. The danger is from the dried up carbon that remains, which in itself is flammable (much more than wood)

There is another problem with transformer (or really any electrics) in the attic : In the summer it gets extremely hot there. The transformer will be overheating just from the high ambient temperature + its normal operation temperature rise

The ballast is chosen according to run current. It will reduce starting torque, so the fan will take longer to get to speed. Is this a problem ?

The motor has already reduced torque by the high slip frequency, so reducing the field means it would become too low.
The rotor resistance is designed so the motor torque barely follows the aerodynamic drag, so maintains barely enough reserve to start. Any further reduction and the motor may easily get stuck in some low rpm high slip mode, overheating both tge stator winding, as well as the rotor cage.
The thing is the rotor resistance causes slip losses when running, so to keep losses low it must be as low as possible. But at the same time the resistance should be high enough so the field wont be pushed away from the rotor (at high slip frequencies, so low rotor speed) so it will be able to start fully. The design is then a careful balance for the given application.
The fact it is just a single and not three phase motor makes it even worse, the same result has the typical ceiling fan format of a very short, large diameter and high number of pole pairs low rpm machine, where the gap has to be rather large compare to the pole spacing and motor length, to make sure even manufacturing tolerances and some bearing wear wont cause the rotor crashing into the stator.

Running a transformer in the attic can perfectly reach 100 degrees  Celsius at normal work in summer, which is a self ignitor and it will end on fire one way or another, also, big transformers are submerged in oil, which can end in a big disaster as seen on this video.

Running a transformer in the attic can perfectly reach 100 degrees  Celsius at normal work in summer, which is a self ignitor and it will end on fire one way or another, also, big transformers are submerged in oil, which can end in a big disaster as seen on this video.

We are talking about a transformer for a single fan, not for a train locomotive...
So about 1..2kg with deltaT barely 20degC. And of course with a tgermal cutout device.

Something like the size of a microwave transformer on the attic shouldn't be any problem, but I would add an insulation plate for protect the wood.

Something like the size of a microwave transformer on the attic shouldn't be any problem, but I would add an insulation plate for protect the wood.

About 10x lower power rating will be way sufficient...